Nebius AI at the frontiers of physics and maths

Donated computing time is helping researchers at the London Institute model the universe and formulate new conjectures.

While theoretical research typically requires nothing more than chalk and a blackboard, it sometimes helps to form our intuition by doing simple numerical experiments. But recently, a new way of guiding discovery has emerged: using AI to look for unexpected patterns as a basis for forming new conjectures. Because in mathematics there are no coincidences, and mathematical data is cheap, the field is the ideal testing ground for AI-assisted discovery, as we argued in Nature. At the London Institute for Mathematical Sciences, we are at the cutting-edge of exploiting machine learning to make progress in fundamental science.

Which is why we are thrilled, as well as extremely grateful, to learn that Nebius AI is providing cloud computing resources to us for the use of our scientists.

Example one. Our Fellow Dr Evgeny Sobko will invest the Nebius compute time in his ground-breaking research on quantum integrable models. While these models do not represent ‘real world’ quantum systems, they possess high degrees of symmetry, allowing the equations that describe them to be solved exactly. As such, they are of immense importance as a playground for the development of new ideas, intuitions, and techniques that can be applied in other areas of physics and maths. Unfortunately, there is no easy way of knowing whether a quantum model will be integrable or of finding ones that are.

In work first presented in June last year, Dr Sobko and his collaborators unveiled a neural network that can explore different quantum systems, automatically detect integrable models and solve them numerically. This was the first time machine learning had been applied to the problem. Now they are trying to use the numerical data to find exact formulae that describe the models. With relatively minor modifications, he says, the same approach could be used to hunt for integrable models in quantum field or string theories.

Example two. The research of Dr Mikhail Burtsev, our Landau AI Fellow, spans several key areas that will benefit from access to extra computing capacity. With his collaborators, Dr Burtsev has invented a way to dramatically increase the input context size of transformers, the neural network architecture underlying the sort of large language models that power ChatGPT. The work was cited by researchers at Google, working on Gemini, the firm’s most advanced AI models. Dr Burtsev also helped to develop one of the first DNA language models, GENA-LM, which can interpret much longer input genetic sequences than existing tools, as well as a user-friendly web-based service for geneticists and clinicians to use.

With the GPU time awarded by Nebius AI, Dr Burtsev hopes to advance his work on knowledge graphs—interlinked, organised networks of facts that underlie web searches like Google’s, and structure the data used by Wikipedia. His team is working on improving how data is captured in knowledge graphs, with the aim of making them more accurate and the process more efficient. Their goal is to develop AI models for mathematics that can learn complex numeric patterns and dependencies and so catalyse new discoveries in mathematics and theoretical physics.

Example three. Our Fellow Prof. Yang-Hui He is a pioneer in the area of AI-driven pure mathematics and theoretical physics, with a forthcoming article on this fast-moving field for Nature Reviews Physics. With his collaborators, Prof. He is using artificial intelligence techniques to help find universes like ours from the vast number of possibilities that string theory offers. For example, the number of candidate Calabi-Yau geometries are in their billions, and going through them all by hand is not feasible.

Prof. He has also used machine-learning to help raise conjectures in pure mathematics. For instance, one recent breakthrough was the discovery of the Murmuration Conjectures in number theory, which was found by data-mining millions of elliptic curves. These murmurations of elliptic curves may provide clues to a proof of the Birch-Swinnerton-Dyer Conjecture, recognised as one of the toughest problems in modern mathematics and one of the seven Millennium Prize Problems.

Example four. A metascience project, led by our developer Andrey Fedosyeyev, will use large language models and related techniques to analyse the abstracts of the thousands of active UKRI grants, and the hundreds of thousands of papers on the arXiv preprint server. By computing the semantic distance between every pair of grants and papers, we will be able to automatically cluster grants and papers by subject, map out the landscape of research fields, and identify the research that is most-closely related to a given project or idea. The project aims to provide the government, funding bodies, businesses and research organisations with a rigorous, detailed and empirical overview of the research landscape.

As a preliminary step, Mr Fedosyeyev has already created an arXiv search tool by collecting data from approximately 100,000 papers in two subfields with which our institute has specific expertise: high energy physics theory and statistical mechanics. Extra compute time will allow him to complete the project, which will offer unparalleled resources for dynamic horizon-scanning and surveying, investigating and shaping the national and global production of scientific knowledge.

If you also work in academia, advance in AI subdomains, and feel a shortage of GPU resources, check out the Nebius AI Research Grant program, through which we’ve received H100s and other graphics cards for the mentioned projects.

Counterintuitively, machine learning can sometimes be of benefit in theoretical physics and mathematics. Thanks to the infrastructure provided by Nebius AI, we have been able to speed up our research in areas from the creation of mathematical conjectures to synthesising data on the process of science itself.