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LLMs for knowledge graph construction and reasoning: recent capabilities and future opportunities

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Website Developmemt Technologies: A Review

Abstract: Service Science is that the basis of knowledge system and net services that judge to the provider/client model. This paper developments a technique which will be utilized in the event of net services like websites, net applications and eCommerce. The goal is to development a technique that may add structure to a extremely unstructured drawback to help within the development and success of net services. The new methodology projected are going to be referred to as {the net|the online|the net} Development Life Cycle (WDLC) and tailored from existing methodologies and applied to the context of web development. This paper can define well the projected phases of the WDLC. Keywords: Web Development, Application Development, Technologies, eCommerce.

Analysis of Russian Segment of the Web Development Market Operating Online on Upwork

The Russian segment of the web services market in the online environment, on the platform of the Upwork freelance exchange, is considered, its key characteristics, the composition of participants, development trends are highlighted, and the market structure is identified. It is found that despite the low barriers to entry, the web development market is very stable, since the composition of entrenched firms that have been operating for more than six years remains. The pricing policy of most Russian companies indicates that they work in the middle price segment and have low budgets, which is due to the specifics of the foreign market and high competition.

Farming Assistant Web Services: Agricultor

Abstract: Our farming assistant web services provides assistance to new as well as establish farmers to get the solutions to dayto-day problems faced in the field. A farmer gets to connect with other farmers throughout India to get more information about a particular crop which is popular in other states. Keywords: Farmers, Assistance, Web Development

Tradução de ementas e histórico escolar para o inglês: contribuição para participação de discentes do curso técnico em informática para internet integrado ao ensino médio em programas de mobilidade acadêmica / Translation of summary and school records into english: contribution to the participation of high school with associate technical degree on web development students in academic mobility programs

Coded websites vs wordpress websites.

This document gives multiple instructions related to web developers using older as well as newer technology. Websites are being created using newer technologies like wordpress whereas on the other hand many people prefer making websites using the traditional way. This document will clear the doubt whether an individual should use wordpress websites or coded websites according to the users convenience. The Responsiveness of the websites, the use of CMS nowadays, more and more up gradation of technologies with SEO, themes, templates, etc. make things like web development much much easier. The aesthetics, the culture, the expressions, the features all together add up in order make the designing and development a lot more efficient and effective. Digital Marketing has a tremendous growth over the last two years and yet shows no signs of stopping, is closely related with the web development environment. Nowadays all businesses are going online due to which the impact of web development has become such that it has become an integral part of any online business.

Cognitive disabilities and web accessibility: a survey into the Brazilian web development community

Cognitive disabilities include a diversity of conditions related to cognitive functions, such as reading, understanding, learning, solving problems, memorization and speaking. They differ largely from each other, making them a heterogeneous complex set of disabilities. Although the awareness about cognitive disabilities has been increasing in the last few years, it is still less than necessary compared to other disabilities. The need for an investigation about this issue is part of the agenda of the Challenge 2 (Accessibility and Digital Inclusion) from GranDIHC-Br. This paper describes the results of an online exploratory survey conducted with 105 web development professionals from different sectors to understand their knowledge and barriers regarding accessibility for people with cognitive disabilities. The results evidenced three biases that potentially prevent those professionals from approaching cogni-tive disabilities: strong organizational barriers; difficulty to understand user needs related to cognitive disabilities; a knowledge gap about web accessibility principles and guidelines. Our results confirmed that web development professionals are unaware about cognitive disabilities mostly by a lack of knowledge about them, even if they understand web accessibility in a technical level. Therefore, we suggest that applied research studies focus on how to fill this knowledge gap before providing tools, artifacts or frameworks.

PERANCANGAN WEB RESPONSIVE UNTUK SISTEM INFORMASI OBAT-OBATAN

A good information system must not only be neat, effective, and resilient, but also must be user friendly and up to date. In a sense, it is able to be applied to various types of electronic devices, easily accessible at any whereand time (real time), and can be modified according to user needs in a relatively easy and simple way. Information systems are now needed by various parties, especially in the field of administration and sale of medicines for Cut Nyak Dhien Hospital. During this time, recording in books has been very ineffective and caused many problems, such as difficulty in accessing old data, asa well as the information obtained was not real time. To solve it, this research raises the theme of the appropriate information system design for the hospital concerned, by utilizing CSS Bootstrap framework and research methodology for web development, namely Web Development Life Cycle. This research resulted in a responsive system by providing easy access through desktop computers, tablets, and smartphones so that it would help the hospital in the data processing process in real time.

Web Development and performance comparison of Web Development Technologies in Node.js and Python

“tom had us all doing front-end web development”: a nostalgic (re)imagining of myspace, assessment of site classifications according to layout type in web development, export citation format, share document.

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Reference management. Clean and simple.

The top list of academic search engines

1. Google Scholar

4. science.gov, 5. semantic scholar, 6. baidu scholar, get the most out of academic search engines, frequently asked questions about academic search engines, related articles.

Academic search engines have become the number one resource to turn to in order to find research papers and other scholarly sources. While classic academic databases like Web of Science and Scopus are locked behind paywalls, Google Scholar and others can be accessed free of charge. In order to help you get your research done fast, we have compiled the top list of free academic search engines.

Google Scholar is the clear number one when it comes to academic search engines. It's the power of Google searches applied to research papers and patents. It not only lets you find research papers for all academic disciplines for free but also often provides links to full-text PDF files.

• Coverage: approx. 200 million articles
• Abstracts: only a snippet of the abstract is available
• Related articles: ✔
• References: ✔
• Cited by: ✔
• Links to full text: ✔
• Export formats: APA, MLA, Chicago, Harvard, Vancouver, RIS, BibTeX

BASE is hosted at Bielefeld University in Germany. That is also where its name stems from (Bielefeld Academic Search Engine).

• Coverage: approx. 136 million articles (contains duplicates)
• Abstracts: ✔
• Related articles: ✘
• References: ✘
• Cited by: ✘
• Export formats: RIS, BibTeX

CORE is an academic search engine dedicated to open-access research papers. For each search result, a link to the full-text PDF or full-text web page is provided.

• Coverage: approx. 136 million articles
• Links to full text: ✔ (all articles in CORE are open access)
• Export formats: BibTeX

Science.gov is a fantastic resource as it bundles and offers free access to search results from more than 15 U.S. federal agencies. There is no need anymore to query all those resources separately!

• Coverage: approx. 200 million articles and reports
• Links to full text: ✔ (available for some databases)
• Export formats: APA, MLA, RIS, BibTeX (available for some databases)

Semantic Scholar is the new kid on the block. Its mission is to provide more relevant and impactful search results using AI-powered algorithms that find hidden connections and links between research topics.

• Coverage: approx. 40 million articles
• Export formats: APA, MLA, Chicago, BibTeX

Although Baidu Scholar's interface is in Chinese, its index contains research papers in English as well as Chinese.

• Coverage: no detailed statistics available, approx. 100 million articles
• Abstracts: only snippets of the abstract are available
• Export formats: APA, MLA, RIS, BibTeX

RefSeek searches more than one billion documents from academic and organizational websites. Its clean interface makes it especially easy to use for students and new researchers.

• Coverage: no detailed statistics available, approx. 1 billion documents
• Abstracts: only snippets of the article are available
• Export formats: not available

Consider using a reference manager like Paperpile to save, organize, and cite your references. Paperpile integrates with Google Scholar and many popular databases, so you can save references and PDFs directly to your library using the Paperpile buttons:

Google Scholar is an academic search engine, and it is the clear number one when it comes to academic search engines. It's the power of Google searches applied to research papers and patents. It not only let's you find research papers for all academic disciplines for free, but also often provides links to full text PDF file.

Semantic Scholar is a free, AI-powered research tool for scientific literature developed at the Allen Institute for AI. Sematic Scholar was publicly released in 2015 and uses advances in natural language processing to provide summaries for scholarly papers.

BASE , as its name suggest is an academic search engine. It is hosted at Bielefeld University in Germany and that's where it name stems from (Bielefeld Academic Search Engine).

CORE is an academic search engine dedicated to open access research papers. For each search result a link to the full text PDF or full text web page is provided.

Science.gov is a fantastic resource as it bundles and offers free access to search results from more than 15 U.S. federal agencies. There is no need any more to query all those resources separately!

“The only truly modern academic research engine”

Oa.mg is a search engine for academic papers, specialising in open access. we have over 250 million papers in our index..

🇺🇦    make metadata, not war

A comprehensive bibliographic database of the world’s scholarly literature

The world’s largest collection of open access research papers, machine access to our vast unique full text corpus, core features, indexing the world’s repositories.

We serve the global network of repositories and journals

Comprehensive data coverage

We provide both metadata and full text access to our comprehensive collection through our APIs and Datasets

Powerful services

We create powerful services for researchers, universities, and industry

Cutting-edge solutions

We research and develop innovative data-driven and AI solutions

Committed to the POSI

Cost-free PIDs for your repository

OAI identifiers are unique identifiers minted cost-free by repositories. Ensure that your repository is correctly configured, enabling the CORE OAI Resolver to redirect your identifiers to your repository landing pages.

OAI IDs provide a cost-free option for assigning Persistent Identifiers (PIDs) to your repository records. Learn more.

Who we serve?

Enabling others to create new tools and innovate using a global comprehensive collection of research papers.

“ Our partnership with CORE will provide Turnitin with vast amounts of metadata and full texts that we can ... ” Show more

Gareth Malcolm, Content Partner Manager at Turnitin

Academic institutions.

Making research more discoverable, improving metadata quality, helping to meet and monitor open access compliance.

“ CORE’s role in providing a unified search of repository content is a great tool for the researcher and ex... ” Show more

Nicola Dowson, Library Services Manager at Open University

Researchers & general public.

Tools to find, discover and explore the wealth of open access research. Free for everyone, forever.

“ With millions of research papers available across thousands of different systems, CORE provides an invalu... ” Show more

Jon Tennant, Rogue Paleontologist and Founder of the Open Science MOOC

Helping funders to analyse, audit and monitor open research and accelerate towards open science.

“ Aggregation plays an increasingly essential role in maximising the long-term benefits of open access, hel... ” Show more

Ben Johnson, Research Policy Adviser at Research England

Our services, access to raw data.

Create new and innovative solutions.

Content discovery

Find relevant research and make your research more visible.

Managing content

Manage how your research content is exposed to the world.

Companies using CORE

Gareth Malcolm

Content Partner Manager at Turnitin

Our partnership with CORE will provide Turnitin with vast amounts of metadata and full texts that we can utilise in our plagiarism detection software.

Academic institution using CORE

Kathleen Shearer

Executive Director of the Confederation of Open Access Repositories (COAR)

CORE has significantly assisted the academic institutions participating in our global network with their key mission, which is their scientific content exposure. In addition, CORE has helped our content administrators to showcase the real benefits of repositories via its added value services.

Partner projects

Ben Johnson

Research Policy Adviser

Aggregation plays an increasingly essential role in maximising the long-term benefits of open access, helping to turn the promise of a 'research commons' into a reality. The aggregation services that CORE provides therefore make a very valuable contribution to the evolving open access environment in the UK.

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A web scraping tool to systematically extract the text of scientific papers and corresponding metadata from university accessible journals.

NLPatVCU/PaperScraper

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Paperscraper.

PaperScraper facilitates the extraction of text and meta-data from scientific journal articles for use in NLP systems. In simplest application, query by the URL of a journal article and receive back a structured JSON object containing the article text and metadata. More robustly, query by relevant attribute tags of articles (ie. DOI, Pubmed ID) and have an article URL automatically found and extracted from.

Retrieve structured journal articles in three lines:

or use a domain-specific aggregator such as PubMed and let PaperScraper automatically find a link for you:

Current Scraping Capabilities

Contribution

To contribute an additional scraper to PaperScraper simply do the following (detailed instructions found in section 'Example Contribution Development Set-up'):

• Fork this repository and clone down a local version of your fork.
• set-up/enter a virtual environment using a Python version of 3.5 or greater.
• Run the setup.py file and verify that all package requirements have successfully installed in your virtual environment.
• Contribute a scraper by adding a file to the paperscraper/scrapers directory following the naming convention '<journal>_scraper.py'. Your scraper should implement the BaseScraper interface and simply include the necessary methods (see other scrapers for examples). The package will handle all other integration of your scraper into the framework.
• PaperScraper utilizes BeautifulSoup4 for navigating markdown. When writing a scraper, each method receives an instance of a BeautifulSoup object that wraps the markdown of the queried website. This markdown is then navigated to retrieve relevant information. See BeautifulSoup documentation and examples .
• While developing a scraper, one should simultaneously be write a test file under tests/scrapers named 'test_<journal>.py' . This will not only allow the concurrent debugging of each method as one develops, but more importantly allow for the identifications of any markdown changes (and resulting scraping errors) the publisher makes after development concludes. We emphasis, writing a test is vital to the longevity of your contribution and subsequently the package. See 'Detailed Contribution Instructions' for a walk-through of testing a contribution.
• Once complete, run all package tests with nosetests and submit a pull request.

Contribution Standards

Follow the following formatting standards when developing a scraper:

• Include all meta-html tags inside of the body such as links (<a>), emphasis <em>, etc. These can be filtered out by the end user but can also serve to provide meaningful information to some systems.
• The OrderedDict containing the paper body should be structured as follows:

Example Contribution Development Set-up

We recommend using an IDE such as PyCharm to facilitate the contribution process. It is available for free if you are affiliated with a university . This contribution walk-through assumes that you are utilizing PyCharm Professional Edition.

• Create a new PyCharm project named 'PaperScraper'. When selecting an interpreter, click the gear icon and create a new virtual environment (venv) in a version of Python greater than 3.5 ( details here ). A Python virtual environment serves to isolate your current development from all python packages and version already installed on your machine.
• Fork this repository, navigate to the directory of your project, and clone your fork into it.
• The PyCharm directory view should now update with all relevant project files. Press the button 'Terminal' in the lower-left corner of the IDE to open up an in-IDE terminal instance local to your project - notice the virtual environment is already set.
• Execute python setup.py to install PaperScraper and its dependencies into your virtual environment.
• Execute python setup.py test to run all tests. Insure that you have an internet connection as some tests require it. Further tests (along with only running single test files) can be executed by the command 'nosetests' ( details here ).
• Create new files '<journal>_scraper.py' and 'test_<journal>.py' in paperscraper/scrapers and tests/scrapers respectively. Model the structure/naming conventions of these files after other files in the directories.
• When testing your contribution-in-progress, run the command 'nosetesting -s <test_file_path>' to test only a single file. The '-s' parameter will allow print statements in your test files to show when tests are run. These should be removed before making a pull request.

Ensure that you have an internet connection before testing. To execute all tests, run the command python setup.py test from the top-level directory. To execute a single test, run the command nosetests -s <test_file_path> . The -s flag will allow print statements to print to console. Please remove all print statements before submitting a pull request.

Check out the Nose testing documentation here .

If you are experiencing errors running tests, make sure Nose is running with a version of python 3.5 or greater. If it is not, it is likely an error with Nose not being installed in your virtual environment. Execute the command pip install nose -I to correctly install it.

When writing tests, cover scraping from a few different correct and incorrect URLs. Also test that there is valid output for key sections such as 'authors' and 'body'. Please follow the naming convention for your test files . Refer to the test_sciencedirect.py file as a template for your own tests.

This package is licensed under the GNU General Public License

Acknowledgments

• Nanoinformatics Vertically Integrated Projects

Contributors 4

• Python 100.0%

• University of Michigan Library
• Research Guides

The Library Research Process, Step-by-Step

• Finding Articles
• Finding & Exploring a Topic
• Finding Books
• Evaluating Sources
• Reading Scholarly Articles
• Understanding & Using a Citation Style

Peer Reviewed and Scholarly Articles

What are they? Peer-reviewed articles, also known as scholarly or refereed articles are papers that describe a research study. 

Why are peer-reviewed articles useful? They report on original research that have been reviewed by other experts before they are accepted for publication, so you can reasonably be assured that they contain valid information. 

How do you find them?  Many of the library's databases contain scholarly articles! You'll find more about searching databases below.

Watch: Peer Review in 3 Minutes

Why watch this video?

We are often told that scholarly and peer-reviewed sources are the most credible, but, it's sometimes hard to understand why they are credible and why we should trust these sources more than others. This video takes an in depth approach at explaining the peer review process. 

Hot Tip: Check out the Reading Scholarly Articles page for guidance on how to read and understand a scholarly article.

Using Library Databases

What Are Library Databases? 

Databases are similar to search engines but primarily search scholarly journals, magazines, newspapers and other sources. Some databases are subject specific while others are multi-disciplinary (searching across multiple fields and content types). 

You can view our most popularly used databases on the Library's Home Page , or view a list of all of our databases organized by subject or alphabetically at  U-M Library Databases .

Popular Multidisciplinary Databases

Many students use ProQuest , JSTOR , and Google Scholar for their initial search needs. These are multi-disciplinary and not subject-specific, and they can supply a very large number of  search results.

Subject-Specific Databases

Some popular subject-specific databases include PsycINFO for psychology and psychiatry related topics and  PubMed for health sciences topics. 

Why Should You Use Library Databases?

Unlike a Google search, the Library Databases will grant you access to high quality credible sources. 

The sources you'll find in library databases include:

• Scholarly journal articles
• Newspaper articles
• Theses & dissertations
• Empirical evidence

Database Filters & Limits Most databases have Filters/Limits. You can use these to narrow down your search to the specific dates, article type, or population that you are researching.

Here is an example of limits in a database, all databases look slightly different but most have these options:

Keywords and Starting a Search

What are Keywords?

• Natural language words that describe your topic 
• Allows for a more flexible search - looks for anywhere the words appear in the record
• Can lead to a broader search, but may yield irrelevant results

Keyword searching  is how we normally start a search. Pull out important words or phrases from your topic to find your keywords.

Tips for Searching with Keywords:

• Example: "climate change"
• Example:  "climate change" AND policy
• Example: comput* will return all words starting with four letters; computing, computer, compute, etc.  
• Example: wom?n will find both woman and women.

What are Subject Headings?

• Pre-defined "controlled vocabulary" that describe what an item is  about 
• Makes for a less flexible search - only the subject fields will be searched
• Targeted search; results are usually more relevant to the topic, but may miss some variations

Subject Terms and/or Headings are pre-defined terms that are used to describe the content of an item. These terms are a controlled vocabulary and function similarly to hashtags on social media. Look carefully at the results from your search. If you find an article that is relevant to the topic you want to write about, take a look at the subject headings. 

Hot Tip: Make a copy of this Google Doc to help you find and develop your topic's keywords.

More Database Recommendations

Need articles for your library research project, but not sure where to start? We recommend these top ten article databases for kicking off your research. If you can't find what you need searching in one of these top ten databases, browse the list of all library databases by subject (academic discipline) or title .

• U-M Library Articles Search This link opens in a new window Use Articles Search to locate scholarly and popular articles, as well as reference works and materials from open access archives.
• ABI/INFORM Global This link opens in a new window Indexes 3,000+ business-related periodicals (with full text for 2,000+), including Wall Street Journal.
• Academic OneFile This link opens in a new window Provides indexing for over 8,000 scholarly journals, industry periodicals, general interest magazines and newspapers.
• Access World News [NewsBank] This link opens in a new window Full text of 600+ U.S. newspapers and 260+ English-language newspapers from other countries worldwide.
• CQ Researcher This link opens in a new window Noted for its in-depth, unbiased coverage of health, social trends, criminal justice, international affairs, education, the environment, technology, and the economy.
• Gale Health and Wellness This link opens in a new window
• Humanities Abstracts (with Full Text) This link opens in a new window Covers 700 periodicals in art, film, journalism, linguistics, music, performing arts, philosophy, religion, history, literature, etc.
• JSTOR This link opens in a new window Full-text access to the archives of 2,600+ journals and 35,000+ books in the arts, humanities, social sciences and sciences.
• ProQuest Research Library This link opens in a new window Indexes over 5,000 journals and magazines, academic and popular, with full text included for over 3,600.
• PsycInfo (APA) This link opens in a new window Premier resource for surveying the literature of psychology and adjunct fields. Covers 1887-present. Produced by the APA.

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• Open access
• Published: 22 July 2024

Neural general circulation models for weather and climate

• Dmitrii Kochkov   ORCID: orcid.org/0000-0003-3846-4911 1   na1 ,
• Janni Yuval   ORCID: orcid.org/0000-0001-7519-0118 1   na1 ,
• Ian Langmore 1   na1 ,
• Peter Norgaard 1   na1 ,
• Jamie Smith 1   na1 ,
• Griffin Mooers 1 ,
• Milan Klöwer 2 ,
• James Lottes 1 ,
• Stephan Rasp 1 ,
• Peter Düben   ORCID: orcid.org/0000-0002-4610-3326 3 ,
• Sam Hatfield 3 ,
• Peter Battaglia 4 ,
• Alvaro Sanchez-Gonzalez 4 ,
• Matthew Willson   ORCID: orcid.org/0000-0002-8730-1927 4 ,
• Michael P. Brenner 1 , 5 &
• Stephan Hoyer   ORCID: orcid.org/0000-0002-5207-0380 1   na1  

Nature volume  632 ,  pages 1060–1066 ( 2024 ) Cite this article

54k Accesses

3 Citations

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• Atmospheric dynamics
• Climate and Earth system modelling
• Computational science

General circulation models (GCMs) are the foundation of weather and climate prediction 1 , 2 . GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting 3 , 4 . However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

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Solving the equations for Earth’s atmosphere with general circulation models (GCMs) is the basis of weather and climate prediction 1 , 2 . Over the past 70 years, GCMs have been steadily improved with better numerical methods and more detailed physical models, while exploiting faster computers to run at higher resolution. Inside GCMs, the unresolved physical processes such as clouds, radiation and precipitation are represented by semi-empirical parameterizations. Tuning GCMs to match historical data remains a manual process 5 , and GCMs retain many persistent errors and biases 6 , 7 , 8 . The difficulty of reducing uncertainty in long-term climate projections 9 and estimating distributions of extreme weather events 10 presents major challenges for climate mitigation and adaptation 11 .

Recent advances in machine learning have presented an alternative for weather forecasting 3 , 4 , 12 , 13 . These models rely solely on machine-learning techniques, using roughly 40 years of historical data from the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis v5 (ERA5) 14 for model training and forecast initialization. Machine-learning methods have been remarkably successful, demonstrating state-of-the-art deterministic forecasts for 1- to 10-day weather prediction at a fraction of the computational cost of traditional models 3 , 4 . Machine-learning atmospheric models also require considerably less code, for example GraphCast 3 has 5,417 lines versus 376,578 lines for the National Oceanic and Atmospheric Administration’s FV3 atmospheric model 15 (see Supplementary Information section  A for details).

Nevertheless, machine-learning approaches have noteworthy limitations compared with GCMs. Existing machine-learning models have focused on deterministic prediction, and surpass deterministic numerical weather prediction in terms of the aggregate metrics for which they are trained 3 , 4 . However, they do not produce calibrated uncertainty estimates 4 , which is essential for useful weather forecasts 1 . Deterministic machine-learning models using a mean-squared-error loss are rewarded for averaging over uncertainty, producing unrealistically blurry predictions when optimized for multi-day forecasts 3 , 13 . Unlike physical models, machine-learning models misrepresent derived (diagnostic) variables such as geostrophic wind 16 . Furthermore, although there has been some success in using machine-learning approaches on longer timescales 17 , 18 , these models have not demonstrated the ability to outperform existing GCMs.

Hybrid models that combine GCMs with machine learning are appealing because they build on the interpretability, extensibility and successful track record of traditional atmospheric models 19 , 20 . In the hybrid model approach, a machine-learning component replaces or corrects the traditional physical parameterizations of a GCM. Until now, the machine-learning component in such models has been trained ‘offline’, by learning parameterizations independently of their interaction with dynamics. These components are then inserted into an existing GCM. The lack of coupling between machine-learning components and the governing equations during training potentially causes serious problems, such as instability and climate drift 21 . So far, hybrid models have mostly been limited to idealized scenarios such as aquaplanets 22 , 23 . Under realistic conditions, machine-learning corrections have reduced some biases of very coarse GCMs 24 , 25 , 26 , but performance remains considerably worse than state-of-the-art models.

Here we present NeuralGCM, a fully differentiable hybrid GCM of Earth’s atmosphere. NeuralGCM is trained on forecasting up to 5-day weather trajectories sampled from ERA5. Differentiability enables end-to-end ‘online training’ 27 , with machine-learning components optimized in the context of interactions with the governing equations for large-scale dynamics, which we find enables accurate and stable forecasts. NeuralGCM produces physically consistent forecasts with accuracy comparable to best-in-class models across a range of timescales, from 1- to 15-day weather to decadal climate prediction.

Neural GCMs

A schematic of NeuralGCM is shown in Fig. 1 . The two key components of NeuralGCM are a differentiable dynamical core for solving the discretized governing dynamical equations and a learned physics module that parameterizes physical processes with a neural network, described in full detail in Methods , Supplementary Information sections  B and C , and Supplementary Table 1 . The dynamical core simulates large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force. The learned physics module (Supplementary Fig. 1 ) predicts the effect of unresolved processes, such as cloud formation, radiative transport, precipitation and subgrid-scale dynamics, on the simulated fields using a neural network.

a , Overall model structure, showing how forcings F t , noise z t (for stochastic models) and inputs y t are encoded into the model state x t . The model state is fed into the dynamical core, and alongside forcings and noise into the learned physics module. This produces tendencies (rates of change) used by an implicit–explicit ordinary differential equation (ODE) solver to advance the state in time. The new model state x t +1 can then be fed back into another time step, or decoded into model predictions. b , The learned physics module, which feeds data for individual columns of the atmosphere into a neural network used to produce physics tendencies in that vertical column.

The differentiable dynamical core in NeuralGCM allows an end-to-end training approach, whereby we advance the model multiple time steps before employing stochastic gradient descent to minimize discrepancies between model predictions and reanalysis (Supplementary Information section  G.2 ). We gradually increase the rollout length from 6 hours to 5 days (Supplementary Information section  G and Supplementary Table 5 ), which we found to be critical because our models are not accurate for multi-day prediction or stable for long rollouts early in training (Supplementary Information section  H.6.2 and Supplementary Fig. 23 ). The extended back-propagation through hundreds of simulation steps enables our neural networks to take into account interactions between the learned physics and the dynamical core. We train deterministic and stochastic NeuralGCM models, each of which uses a distinct training protocol, described in full detail in Methods and Supplementary Table 4 .

We train a range of NeuralGCM models at horizontal resolutions with grid spacing of 2.8°, 1.4° and 0.7° (Supplementary Fig. 7 ). We evaluate the performance of NeuralGCM at a range of timescales appropriate for weather forecasting and climate simulation. For weather, we compare against the best-in-class conventional physics-based weather models, ECMWF’s high-resolution model (ECMWF-HRES) and ensemble prediction system (ECMWF-ENS), and two of the recent machine-learning-based approaches, GraphCast 3 and Pangu 4 . For climate, we compare against a global cloud-resolving model and Atmospheric Model Intercomparison Project (AMIP) runs.

Medium-range weather forecasting

Our evaluation set-up focuses on quantifying accuracy and physical consistency, following WeatherBench2 12 . We regrid all forecasts to a 1.5° grid using conservative regridding, and average over all 732 forecasts made at noon and midnight UTC in the year 2020, which was held-out from training data for all machine-learning models. NeuralGCM, GraphCast and Pangu compare with ERA5 as the ground truth, whereas ECMWF-ENS and ECMWF-HRES compare with the ECMWF operational analysis (that is, HRES at 0-hour lead time), to avoid penalizing the operational forecasts for different biases than ERA5.

Model accuracy

We use ECMWF’s ensemble (ENS) model as a reference baseline as it achieves the best performance across the majority of lead times 12 . We assess accuracy using (1) root-mean-squared error (RMSE), (2) root-mean-squared bias (RMSB), (3) continuous ranked probability score (CRPS) and (4) spread-skill ratio, with the results shown in Fig. 2 . We provide more in-depth evaluations including scorecards, metrics for additional variables and levels and maps in Extended Data Figs. 1 and 2 , Supplementary Information section  H and Supplementary Figs. 9 – 22 .

a , c , RMSE ( a ) and RMSB ( c ) for ECMWF-ENS, ECMWF-HRES, NeuralGCM-0.7°, NeuralGCM-ENS, GraphCast 3 and Pangu 4 on headline WeatherBench2 variables, as a percentage of the error of ECMWF-ENS. Deterministic and stochastic models are shown in solid and dashed lines respectively. e , g , CRPS relative to ECMWF-ENS ( e ) and spread-skill ratio for the ENS and NeuralGCM-ENS models ( g ). b , d , f , h , Spatial distributions of RMSE ( b ), bias ( d ), CRPS ( f ) and spread-skill ratio ( h ) for NeuralGCM-ENS and ECMWF-ENS models for 10-day forecasts of specific humidity at 700 hPa. Spatial plots of RMSE and CRPS show skill relative to a probabilistic climatology 12 with an ensemble member for each of the years 1990–2019. The grey areas indicate regions where climatological surface pressure on average is below 700 hPa.

Deterministic models that produce a single weather forecast for given initial conditions can be compared effectively using RMSE skill at short lead times. For the first 1–3 days, depending on the atmospheric variable, RMSE is minimized by forecasts that accurately track the evolution of weather patterns. At this timescale we find that NeuralGCM-0.7° and GraphCast achieve best results, with slight variations across different variables (Fig. 2a ). At longer lead times, RMSE rapidly increases owing to chaotic divergence of nearby weather trajectories, making RMSE less informative for deterministic models. RMSB calculates persistent errors over time, which provides an indication of how models would perform at much longer lead times. Here NeuralGCM models also compare favourably against previous approaches (Fig. 2c ), with notably much less bias for specific humidity in the tropics (Fig. 2d ).

Ensembles are essential for capturing intrinsic uncertainty of weather forecasts, especially at longer lead times. Beyond about 7 days, the ensemble means of ECMWF-ENS and NeuralGCM-ENS forecasts have considerably lower RMSE than the deterministic models, indicating that these models better capture the average of possible weather. A better metric for ensemble models is CRPS, which is a proper scoring rule that is sensitive to full marginal probability distributions 28 . Our stochastic model (NeuralGCM-ENS) running at 1.4° resolution has lower error compared with ECMWF-ENS across almost all variables, lead times and vertical levels for ensemble-mean RMSE, RSMB and CRPS (Fig. 2a,c,e and Supplementary Information section  H ), with similar spatial patterns of skill (Fig. 2b,f ). Like ECMWF-ENS, NeuralGCM-ENS has a spread-skill ratio of approximately one (Fig. 2d ), which is a necessary condition for calibrated forecasts 29 .

An important characteristic of forecasts is their resemblance to realistic weather patterns. Figure 3 shows a case study that illustrates the performance of NeuralGCM on three types of important weather phenomenon: tropical cyclones, atmospheric rivers and the Intertropical Convergence Zone. Figure 3a shows that all the machine-learning models make significantly blurrier forecasts than the source data ERA5 and physics-based ECMWF-HRES forecast, but NeuralCGM-0.7° outperforms the pure machine-learning models, despite its coarser resolution (0.7° versus 0.25° for GraphCast and Pangu). Blurry forecasts correspond to physically inconsistent atmospheric conditions and misrepresent extreme weather. Similar trends hold for other derived variables of meteorological interest (Supplementary Information section  H.2 ). Ensemble-mean predictions, from both NeuralGCM and ECMWF, are closer to ERA5 in an average sense, and thus are inherently smooth at long lead times. In contrast, as shown in Fig. 3 and in Supplementary Information section  H.3 , individual realizations from the ECMWF and NeuralGCM ensembles remain sharp, even at long lead times. Like ECMWF-ENS, NeuralGCM-ENS produces a statistically representative range of future weather scenarios for each weather phenomenon, despite its eight-times-coarser resolution.

All forecasts are initialized at 2020-08-22T12z, chosen to highlight Hurricane Laura, the most damaging Atlantic hurricane of 2020. a , Specific humidity at 700 hPa for 1-day, 5-day and 10-day forecasts over North America and the Northeast Pacific Ocean from ERA5 14 , ECMWF-HRES, NeuralGCM-0.7°, ECMWF-ENS (mean), NeuralGCM-ENS (mean), GraphCast 3 and Pangu 4 . b , Forecasts from individual ensemble members from ECMWF-ENS and NeuralGCM-ENS over regions of interest, including predicted tracks of Hurricane Laura from each of the 50 ensemble members (Supplementary Information section  I.2 ). The track from ERA5 is plotted in black.

We can quantify the blurriness of different forecast models via their power spectra. Supplementary Figs. 17 and 18 show that the power spectra of NeuralCGM-0.7° is consistently closer to ERA5 than the other machine-learning forecast methods, but is still blurrier than ECMWF’s physical forecasts. The spectra of NeuralGCM forecasts is also roughly constant over the forecast period, in stark contrast to GraphCast, which worsens with lead time. The spectrum of NeuralGCM becomes more accurate with increased resolution (Supplementary Fig. 22 ), which suggests the potential for further improvements of NeuralGCM models trained at higher resolutions.

Water budget

In NeuralGCM, advection is handled by the dynamical core, while the machine-learning parameterization models local processes within vertical columns of the atmosphere. Thus, unlike pure machine-learning methods, local sources and sinks can be isolated from tendencies owing to horizontal transport and other resolved dynamics (Supplementary Fig. 3 ). This makes our results more interpretable and facilitates the diagnosis of the water budget. Specifically, we diagnose precipitation minus evaporation (Supplementary Information section  H.5 ) rather than directly predicting these as in machine-learning-based approaches 3 . For short weather forecasts, the mean of precipitation minus evaporation has a realistic spatial distribution that is very close to ERA5 data (Extended Data Fig. 4c–e ). The precipitation-minus-evaporation rate distribution of NeuralGCM-0.7° closely matches the ERA5 distribution in the extratropics (Extended Data Fig. 4b ), although it underestimates extreme events in the tropics (Extended Data Fig. 4a ). It is noted that the current version of NeuralGCM directly predicts tendencies for an atmospheric column, and thus cannot distinguish between precipitation and evaporation.

Geostrophic wind balance

We examined the extent to which NeuralGCM, GraphCast and ECMWF-HRES capture the geostrophic wind balance, the near-equilibrium between the dominant forces that drive large-scale dynamics in the mid-latitudes 30 . A recent study 16 highlighted that Pangu misrepresents the vertical structure of the geostrophic and ageostrophic winds and noted a deterioration at longer lead times. Similarly, we observe that GraphCast shows an error that worsens with lead time. In contrast, NeuralGCM more accurately depicts the vertical structure of the geostrophic and ageostrophic winds, as well as their ratio, compared with GraphCast across various rollouts, when compared against ERA5 data (Extended Data Fig. 3 ). However, ECMWF-HRES still shows a slightly closer alignment to ERA5 data than NeuralGCM does. Within NeuralGCM, the representation of the geostrophic wind’s vertical structure only slightly degrades in the initial few days, showing no noticeable changes thereafter, particularly beyond day 5.

Generalizing to unseen data

Physically consistent weather models should still perform well for weather conditions for which they were not trained. We expect that NeuralGCM may generalize better than machine-learning-only atmospheric models, because NeuralGCM employs neural networks that act locally in space, on individual vertical columns of the atmosphere. To explore this hypothesis, we compare versions of NeuralCGM-0.7° and GraphCast trained to 2017 on 5 years of weather forecasts beyond the training period (2018–2022) in Supplementary Fig. 36 . Unlike GraphCast, NeuralGCM does not show a clear trend of increasing error when initialized further into the future from the training data. To extend this test beyond 5 years, we trained a NeuralGCM-2.8° model using only data before 2000, and tested its skill for over 21 unseen years (Supplementary Fig. 35 ).

Climate simulations

Although our deterministic NeuralGCM models are trained to predict weather up to 3 days ahead, they are generally capable of simulating the atmosphere far beyond medium-range weather timescales. For extended climate simulations, we prescribe historical sea surface temperature (SST) and sea-ice concentration. These simulations feature many emergent phenomena of the atmosphere on timescales from months to decades.

For climate simulations with NeuralGCM, we use 2.8° and 1.4° deterministic models, which are relatively inexpensive to train (Supplementary Information section  G.7 ) and allow us to explore a larger parameter space to find stable models. Previous studies found that running extended simulations with hybrid models is challenging due to numerical instabilities and climate drift 21 . To quantify stability in our selected models, we run multiple initial conditions and report how many of them finish without instability.

Seasonal cycle and emergent phenomena

To assess the capability of NeuralGCM to simulate various aspects of the seasonal cycle, we run 2-year simulations with NeuralGCM-1.4°. for 37 different initial conditions spaced every 10 days for the year 2019. Out of these 37 initial conditions, 35 successfully complete the full 2 years without instability; for case studies of instability, see Supplementary Information section  H.7 , and Supplementary Figs. 26 and 27 . We compare results from NeuralGCM-1.4° for 2020 with ERA5 data and with outputs from the X-SHiELD global cloud-resolving model, which is coupled to an ocean model nudged towards reanalysis 31 . This X-SHiELD run has been used as a target for training machine-learning climate models 24 . For comparison, we evaluate models after regridding predictions to 1.4° resolution. This comparison slightly favours NeuralGCM because NeuralGCM was tuned to match ERA5, but the discrepancy between ERA5 and the actual atmosphere is small relative to model error.

Figure 4a shows the temporal variation of the global mean temperature to 2020, as captured by 35 simulations from NeuralGCM, in comparison with the ERA5 reanalysis and standard climatology benchmarks. The seasonality and variability of the global mean temperature from NeuralGCM are quantitatively similar to those observed in ERA5. The ensemble-mean temperature RMSE for NeuralGCM stands at 0.16 K when benchmarked against ERA5, which is a significant improvement over the climatology’s RMSE of 0.45 K. We find that NeuralGCM accurately simulates the seasonal cycle, as evidenced by metrics such as the annual cycle of the global precipitable water (Supplementary Fig. 30a ) and global total kinetic energy (Supplementary Fig. 30b ). Furthermore, the model captures essential atmospheric dynamics, including the Hadley circulation and the zonal-mean zonal wind (Supplementary Fig. 28 ), as well as the spatial patterns of eddy kinetic energy in different seasons (Supplementary Fig. 31 ), and the distinctive seasonal behaviours of monsoon circulation (Supplementary Fig. 29 ; additional details are provided in Supplementary Information section  I.1 ).

a , Global mean temperature for ERA5 14 (orange), 1990–2019 climatology (black) and NeuralGCM-1.4° (blue) for 2020 using 35 simulations initialized every 10 days during 2019 (thick line, ensemble mean; thin lines, different initial conditions). b , Yearly global mean temperature for ERA5 (orange), mean over 22 CMIP6 AMIP experiments 34 (violet; model details are in Supplementary Information section  I.3 ) and NeuralGCM-2.8° for 22 AMIP-like simulations with prescribed SST initialized every 10 days during 1980 (thick line, ensemble mean; thin lines, different initial conditions). c , The RMSB of the 850-hPa temperature averaged between 1981 and 2014 for 22 NeuralGCM-2.8° AMIP runs (labelled NGCM), 22 CMIP6 AMIP experiments (labelled AMIP) and debiased 22 CMIP6 AMIP experiments (labelled AMIP*; bias was removed by removing the 850-hPa global temperature bias). In the box plots, the red line represents the median. The box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. d , Vertical profiles of tropical (20° S–20° N) temperature trends for 1981–2014. Orange, ERA5; black dots, Radiosonde Observation Correction using Reanalyses (RAOBCORE) 41 ; blue dots, mean trends for NeuralGCM; purple dots, mean trends from CMIP6 AMIP runs (grey and black whiskers, 25th and 75th percentiles for NeuralGCM and CMIP6 AMIP runs, respectively). e – g , Tropical cyclone tracks for ERA5 ( e ), NeuralGCM-1.4° ( f ) and X-SHiELD 31 ( g ). h – k , Mean precipitable water for ERA5 ( h ) and the precipitable water bias in NeuralGCM-1.4° ( i ), initialized 90 days before mid-January 2020 similarly to X-SHiELD, X-SHiELD ( j ) and climatology ( k ; averaged between 1990 and 2019). In d – i , quantities are calculated between mid-January 2020 and mid-January 2021 and all models were regridded to a 256 × 128 Gaussian grid before computation and tracking.

Next, we compare the annual biases of a single NeuralGCM realization with a single realization of X-SHiELD (the only one available), both initiated in mid-October 2019. We consider 19 January 2020 to 17 January 2021, the time frame for which X-SHiELD data are available. Global cloud-resolving models, such as X-SHiELD, are considered state of the art, especially for simulating the hydrological cycle, owing to their resolution being capable of resolving deep convection 32 . The annual bias in precipitable water for NeuralGCM (RMSE of 1.09 mm) is substantially smaller than the biases of both X-SHiELD (RMSE of 1.74 mm) and climatology (RMSE of 1.36 mm; Fig. 4i–k ). Moreover, NeuralGCM shows a lower temperature bias in the upper and lower troposphere than X-SHiELD (Extended Data Fig. 6 ). We also indirectly compare precipitation bias in X-SHiELD with precipitation-minus-evaporation bias in NeuralGCM-1.4°, which shows slightly larger bias and grid-scale artefacts for NeuralGCM (Extended Data Fig. 5 ).

Finally, to assess the capability of NeuralGCM to generate tropical cyclones in an annual model integration, we use the tropical cyclone tracker TempestExtremes 33 , as described in Supplementary Information section   I.2 , Supplementary Fig. 34 and Supplementary Table 6 . Figure 4e–g shows that NeuralGCM, even at a coarse resolution of 1.4°, produces realistic trajectories and counts of tropical cyclone (83 versus 86 in ERA5 for the corresponding period), whereas X-SHiELD, when regridded to 1.4° resolution, substantially underestimates the tropical cyclone count (40). Additional statistical analyses of tropical cyclones can be found in Extended Data Figs. 7 and 8 .

Decadal simulations

To assess the capability of NeuralGCM to simulate historical temperature trends, we conduct AMIP-like simulations over a duration of 40 years with NeuralGCM-2.8°. Out of 37 different runs with initial conditions spaced every 10 days during the year 1980, 22 simulations were stable for the entire 40-year period, and our analysis focuses on these results. We compare with 22 simulations run with prescribed SST from the Coupled Model Intercomparison Project Phase 6 (CMIP6) 34 , listed in Supplementary Information section  I.3 .

We find that all 40-year simulations of NeuralGCM, as well as the mean of the 22 AMIP runs, accurately capture the global warming trends observed in ERA5 data (Fig. 4b ). There is a strong correlation in the year-to-year temperature trends with ERA5 data, suggesting that NeuralGCM effectively captures the impact of SST forcing on climate. When comparing spatial biases averaged over 1981–2014, we find that all 22 NeuralGCM-2.8° runs have smaller bias than the CMIP6 AMIP runs, and this result remains even when removing the global temperature bias in CMIP6 AMIP runs (Fig. 4c and Supplementary Figs. 32 and 33 ).

Next, we investigated the vertical structure of tropical warming trends, which climate models tend to overestimate in the upper troposphere 35 . As shown in Fig. 4d , the trends, calculated by linear regression, of NeuralGCM are closer to ERA5 than those of AMIP runs. In particular, the bias in the upper troposphere is reduced. However, NeuralGCM does show a wider spread in its predictions than the AMIP runs, even at levels near the surface where temperatures are typically more constrained by prescribed SST.

Lastly, we evaluated NeuralGCM’s capability to generalize to unseen warmer climates by conducting AMIP simulations with increased SST (Supplementary Information section  I.4.2 ). We find that NeuralGCM shows some of the robust features of climate warming response to modest SST increases (+1 K and +2 K); however, for more substantial SST increases (+4 K), NeuralGCM’s response diverges from expectations (Supplementary Fig. 37 ). In addition, AMIP simulations with increased SST show climate drift, underscoring NeuralGCM’s limitations in this context (Supplementary Fig. 38 ).

NeuralGCM is a differentiable hybrid atmospheric model that combines the strengths of traditional GCMs with machine learning for weather forecasting and climate simulation. To our knowledge, NeuralGCM is the first machine-learning-based model to make accurate ensemble weather forecasts, with better CRPS than state-of-the-art physics-based models. It is also, to our knowledge, the first hybrid model that achieves comparable spatial bias to global cloud-resolving models, can simulate realistic tropical cyclone tracks and can run AMIP-like simulations with realistic historical temperature trends. Overall, NeuralGCM demonstrates that incorporating machine learning is a viable alternative to building increasingly detailed physical models 32 for improving GCMs.

Compared with traditional GCMs with similar skill, NeuralGCM is computationally efficient and low complexity. NeuralGCM runs at 8- to 40-times-coarser horizontal resolution than ECMWF’s Integrated Forecasting System and global cloud-resolving models, which enables 3 to 5 orders of magnitude savings in computational resources. For example, NeuralGCM-1.4° simulates 70,000 simulation days in 24 hours using a single tensor-processing-unit versus 19 simulated days on 13,824 central-processing-unit cores with X-SHiELD (Extended Data Table 1 ). This can be leveraged for previously impractical tasks such as large ensemble forecasting. NeuralGCM’s dynamical core uses global spectral methods 36 , and learned physics is parameterized with fully connected neural networks acting on single vertical columns. Substantial headroom exists to pursue higher accuracy using advanced numerical methods and machine-learning architectures.

Our results provide strong evidence for the disputed hypothesis 37 , 38 , 39 that learning to predict short-term weather is an effective way to tune parameterizations for climate. NeuralGCM models trained on 72-hour forecasts are capable of realistic multi-year simulation. When provided with historical SSTs, they capture essential atmospheric dynamics such as seasonal circulation, monsoons and tropical cyclones. However, we will probably need alternative training strategies 38 , 39 to learn important processes for climate with subtle impacts on weather timescales, such as a cloud feedback.

The NeuralGCM approach is compatible with incorporating either more physics or more machine learning, as required for operational weather forecasts and climate simulations. For weather forecasting, we expect that end-to-end learning 40 with observational data will allow for better and more relevant predictions, including key variables such as precipitation. Such models could include neural networks acting as corrections to traditional data assimilation and model diagnostics. For climate projection, NeuralGCM will need to be reformulated to enable coupling with other Earth-system components (for example, ocean and land), and integrating data on the atmospheric chemical composition (for example, greenhouse gases and aerosols). There are also research challenges common to current machine-learning-based climate models 19 , including the capability to simulate unprecedented climates (that is, generalization), adhering to physical constraints, and resolving numerical instabilities and climate drift. NeuralGCM’s flexibility to incorporate physics-based models (for example, radiation) offers a promising avenue to address these challenges.

Models based on physical laws and empirical relationships are ubiquitous in science. We believe the differentiable hybrid modelling approach of NeuralGCM has the potential to transform simulation for a wide range of applications, such as materials discovery, protein folding and multiphysics engineering design.

Differentiable atmospheric model

NeuralGCM combines components of the numerical solver and flexible neural network parameterizations. Simulation in time is carried out in a coordinate system suitable for solving the dynamical equations of the atmosphere, describing large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force.

Our differentiable dynamical core is implemented in JAX, a library for high-performance code in Python that supports automatic differentiation 42 . The dynamical core solves the hydrostatic primitive equations with moisture, using a horizontal pseudo-spectral discretization and vertical sigma coordinates 36 , 43 . We evolve seven prognostic variables: vorticity and divergence of horizontal wind, temperature, surface pressure, and three water species (specific humidity, and specific ice and liquid cloud water content).

Our learned physics module uses the single-column approach of GCMs 2 , whereby information from only a single atmospheric column is used to predict the impact of unresolved processes occurring within that column. These effects are predicted using a fully connected neural network with residual connections, with weights shared across all atmospheric columns (Supplementary Information section  C.4 ).

The inputs to the neural network include the prognostic variables in the atmospheric column, total incident solar radiation, sea-ice concentration and SST (Supplementary Information section  C.1 ). We also provide horizontal gradients of the prognostic variables, which we found improves performance 44 . All inputs are standardized to have zero mean and unit variance using statistics precomputed during model initialization. The outputs are the prognostic variable tendencies scaled by the fixed unconditional standard deviation of the target field (Supplementary Information section  C.5 ).

To interface between ERA5 14 data stored in pressure coordinates and the sigma coordinate system of our dynamical core, we introduce encoder and decoder components (Supplementary Information section  D ). These components perform linear interpolation between pressure levels and sigma coordinate levels. We additionally introduce learned corrections to both encoder and decoder steps (Supplementary Figs. 4–6 ), using the same column-based neural network architecture as the learned physics module. Importantly, the encoder enables us to eliminate the gravity waves from initialization shock 45 , which otherwise contaminate forecasts.

Figure 1a shows the sequence of steps that NeuralGCM takes to make a forecast. First, it encodes ERA5 data at t  =  t 0 on pressure levels to initial conditions on sigma coordinates. To perform a time step, the dynamical core and learned physics (Fig. 1b ) then compute tendencies, which are integrated in time using an implicit–explicit ordinary differential equation solver 46 (Supplementary Information section  E and Supplementary Table 2 ). This is repeated to advance the model from t  =  t 0 to t  =  t final . Finally, the decoder converts predictions back to pressure levels.

The time-step size of the ODE solver (Supplementary Table 3 ) is limited by the Courant–Friedrichs–Lewy condition on dynamics, and can be small relative to the timescale of atmospheric change. Evaluating learned physics is approximately 1.5 times as expensive as a time step of the dynamical core. Accordingly, following the typical practice for GCMs, we hold learned physics tendencies constant for multiple ODE time steps to reduce computational expense, typically corresponding to 30 minutes of simulation time.

Deterministic and stochastic models

We train deterministic NeuralGCM models using a combination of three loss functions (Supplementary Information section  G.4 ) to encourage accuracy and sharpness while penalizing bias. During the main training phase, all losses are defined in a spherical harmonics basis. We use a standard mean squared error loss for prompting accuracy, modified to progressively filter out contributions from higher total wavenumbers at longer lead times (Supplementary Fig. 8 ). This filtering approach tackles the ‘double penalty problem’ 47 as it prevents the model from being penalized for predicting high-wavenumber features in incorrect locations at later times, especially beyond the predictability horizon. A second loss term encourages the spectrum to match the training data using squared loss on the total wavenumber spectrum of prognostic variables. These first two losses are evaluated on both sigma and pressure levels. Finally, a third loss term discourages bias by adding mean squared error on the batch-averaged mean amplitude of each spherical harmonic coefficient. For analysis of the impact that various loss functions have, refer to Supplementary Information section  H.6.1 , and Supplementary Figs. 23 and 24 . The combined action of the three training losses allow the resulting models trained on 3-day rollouts to remain stable during years-to-decades-long climate simulations. Before final evaluations, we perform additional fine-tuning of just the decoder component on short rollouts of 24 hours (Supplementary Information section  G.5 ).

Stochastic NeuralGCM models incorporate inherent randomness in the form of additional random fields passed as inputs to neural network components. Our stochastic loss is based on the CRPS 28 , 48 , 49 . CRPS consists of mean absolute error that encourages accuracy, balanced by a similar term that encourages ensemble spread. For each variable we use a sum of CRPS in grid space and CRPS in the spherical harmonic basis below a maximum cut-off wavenumber (Supplementary Information section  G.6 ). We compute CRPS on rollout lengths from 6 hours to 5 days. As illustrated in Fig. 1 , we inject noise to the learned encoder and the learned physics module by sampling from Gaussian random fields with learned spatial and temporal correlation (Supplementary Information section  C.2 and Supplementary Fig. 2 ). For training, we generate two ensemble members per forecast, which suffices for an unbiased estimate of CRPS.

Data availability

For training and evaluating the NeuralGCM models, we used the publicly available ERA5 dataset 14 , originally downloaded from https://cds.climate.copernicus.eu/ and available via Google Cloud Storage in Zarr format at gs://gcp-public-data-arco-era5/ar/full_37-1h-0p25deg-chunk-1.zarr-v3. To compare NeuralGCM with operational and data-driven weather models, we used forecast datasets distributed as part of WeatherBench2 12 at https://weatherbench2.readthedocs.io/en/latest/data-guide.html , to which we have added NeuralGCM forecasts for 2020. To compare NeuralGCM with atmospheric models in climate settings, we used CMIP6 data available at https://catalog.pangeo.io/browse/master/climate/ , as well as X-SHiELD 24 outputs available on Google Cloud storage in a ‘requester pays’ bucket at gs://ai2cm-public-requester-pays/C3072-to-C384-res-diagnostics. The Radiosonde Observation Correction using Reanalyses (RAOBCORE) V1.9 that was used as reference tropical temperature trends was downloaded from https://webdata.wolke.img.univie.ac.at/haimberger/v1.9/ . Base maps use freely available data from https://www.naturalearthdata.com/downloads/ .

Code availability

The NeuralGCM code base is separated into two open source projects: Dinosaur and NeuralGCM, both publicly available on GitHub at https://github.com/google-research/dinosaur (ref. 50 ) and https://github.com/google-research/neuralgcm (ref. 51 ). The Dinosaur package implements a differentiable dynamical core used by NeuralGCM, whereas the NeuralGCM package provides machine-learning models and checkpoints of trained models. Evaluation code for NeuralGCM weather forecasts is included in WeatherBench2 12 , available at https://github.com/google-research/weatherbench2 (ref. 52 ).

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Acknowledgements

We thank A. Kwa, A. Merose and K. Shah for assistance with data acquisition and handling; L. Zepeda-Núñez for feedback on the paper; and J. Anderson, C. Van Arsdale, R. Chemke, G. Dresdner, J. Gilmer, J. Hickey, N. Lutsko, G. Nearing, A. Paszke, J. Platt, S. Ponda, M. Pritchard, D. Rothenberg, F. Sha, T. Schneider and O. Voicu for discussions.

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These authors contributed equally: Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Stephan Hoyer

Authors and Affiliations

Google Research, Mountain View, CA, USA

Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Griffin Mooers, James Lottes, Stephan Rasp, Michael P. Brenner & Stephan Hoyer

Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Milan Klöwer

European Centre for Medium-Range Weather Forecasts, Reading, UK

Peter Düben & Sam Hatfield

Google DeepMind, London, UK

Peter Battaglia, Alvaro Sanchez-Gonzalez & Matthew Willson

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Michael P. Brenner

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Contributions

D.K., J.Y., I.L., P.N., J.S. and S. Hoyer contributed equally to this work. D.K., J.Y., I.L., P.N., J.S., G.M., J.L. and S. Hoyer wrote the code. D.K., J.Y., I.L., P.N., G.M. and S. Hoyer trained models and analysed the data. M.P.B. and S. Hoyer managed and oversaw the research project. M.K., S.R., P.D., S. Hatfield, P.B. and M.P.B. contributed technical advice and ideas. M.W. ran experiments with GraphCast for comparison with NeuralGCM. A.S.-G. assisted with data preparation. D.K., J.Y., I.L., P.N. and S. Hoyer wrote the paper. All authors gave feedback and contributed to editing the paper.

Corresponding authors

Correspondence to Dmitrii Kochkov , Janni Yuval or Stephan Hoyer .

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Competing interests.

D.K., J.Y., I.L., P.N., J.S., J.L., S.R., P.B., A.S.-G., M.W., M.P.B. and S. Hoyer are employees of Google. S. Hoyer, D.K., I.L., J.Y., G.M., P.N., J.S. and M.B. have filed international patent application PCT/US2023/035420 in the name of Google LLC, currently pending, relating to neural general circulation models.

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Extended data figures and tables

Extended data fig. 1 maps of bias for neuralgcm-ens and ecmwf-ens forecasts..

Bias is averaged over all forecasts initialized in 2020.

Extended Data Fig. 2 Maps of spread-skill ratio for NeuralGCM-ENS and ECMWF-ENS forecasts.

Spread-skill ratio is averaged over all forecasts initialized in 2020.

Extended Data Fig. 3 Geostrophic balance in NeuralGCM, GraphCast 3 and ECMWF-HRES.

Vertical profiles of the extratropical intensity (averaged between latitude 30°–70° in both hemispheres) and over all forecasts initialized in 2020 of (a,d,g) geostrophic wind, (b,e,h) ageostrophic wind and (c,f,i) the ratio of the intensity of ageostrophic wind over geostrophic wind for ERA5 (black continuous line in all panels), (a,b,c) NeuralGCM-0.7°, (d,e,f) GraphCast and (g,h,i) ECMWF-HRES at lead times of 1 day, 5 days and 10 days.

Extended Data Fig. 4 Precipitation minus evaporation calculated from the third day of weather forecasts.

(a) Tropical (latitudes −20° to 20°) precipitation minus evaporation (P minus E) rate distribution, (b) Extratropical (latitudes 30° to 70° in both hemispheres) P minus E, (c) mean P minus E for 2020 ERA5 14 and (d) NeuralGCM-0.7° (calculated from the third day of forecasts and averaged over all forecasts initialized in 2020), (e) the bias between NeuralGCM-0.7° and ERA5, (f-g) Snapshot of daily precipitation minus evaporation for 2020-01-04 for (f) NeuralGCM-0.7° (forecast initialized on 2020-01-02) and (g) ERA5.

Extended Data Fig. 5 Indirect comparison between precipitation bias in X-SHiELD and precipitation minus evaporation bias in NeuralGCM-1.4°.

Mean precipitation calculated between 2020-01-19 and 2021-01-17 for (a) ERA5 14 (c) X-SHiELD 31 and the biases in (e) X-SHiELD and (g) climatology (ERA5 data averaged over 1990-2019). Mean precipitation minus evaporation calculated between 2020-01-19 and 2021-01-17 for (b) ERA5 (d) NeuralGCM-1.4° (initialized in October 18th 2019) and the biases in (f) NeuralGCM-1.4° and (h) climatology (data averaged over 1990–2019).

Extended Data Fig. 6 Yearly temperature bias for NeuralGCM and X-SHiELD 31 .

Mean temperature between 2020-01-19 to 2020-01-17 for (a) ERA5 at 200hPa and (b) 850hPa. (c,d) the bias in the temperature for NeuralGCM-1.4°, (e,f) the bias in X-SHiELD and (g,h) the bias in climatology (calculated from 1990–2019). NeuralGCM-1.4° was initialized in 18th of October (similar to X-SHiELD).

Extended Data Fig. 7 Tropical Cyclone densities and annual regional counts.

(a) Tropical Cyclone (TC) density from ERA5 14 data spanning 1987–2020. (b) TC density from NeuralGCM-1.4° for 2020, generated using 34 different initial conditions all initialized in 2019. (c) Box plot depicting the annual number of TCs across different regions, based on ERA5 data (1987–2020), NeuralGCM-1.4° for 2020 (34 initial conditions), and orange markers show ERA5 for 2020. In the box plots, the red line represents the median; the box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Extended Data Fig. 8 Tropical Cyclone maximum wind distribution in NeuralGCM vs. ERA5 14 .

Number of Tropical Cyclones (TCs) as a function of maximum wind speed at 850hPa across different regions, based on ERA5 data (1987–2020; in orange), and NeuralGCM-1.4° for 2020 (34 initial conditions; in blue). Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Supplementary information

Supplementary information.

Supplementary Information (38 figures, 6 tables): (A) Lines of code in atmospheric models; (B) Dynamical core of NeuralGCM; (C) Learned physics of NeuralGCM; (D) Encoder and decoder of NeuralGCM; (E) Time integration; (F) Evaluation metrics; (G) Training; (H) Additional weather evaluations; (I) Additional climate evaluations.

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Kochkov, D., Yuval, J., Langmore, I. et al. Neural general circulation models for weather and climate. Nature 632 , 1060–1066 (2024). https://doi.org/10.1038/s41586-024-07744-y

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Accepted : 15 June 2024

Published : 22 July 2024

Issue Date : 29 August 2024

DOI : https://doi.org/10.1038/s41586-024-07744-y

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