# Cohomology, Machine Learning and String Model Building

Lead Research Organisation:
University of Oxford

Department Name: Oxford Physics

### Abstract

The proposed research capitalizes on a newly discovered class of mathematical formulae underpinning the realisation of string theory solutions that unify all known forms of matter and forces. String theory has had a profound impact on the development of both mathematics and physics and, more recently, on the construction of machine learning algorithms.

String theory is a high-energy, extra-dimensional and supersymmetric theory, in which many ideas about physics beyond the Standard Model can be incorporated in a natural way. Although difficult, making contact with experimental physics is an imperative for string theory, requiring a sustained effort in developing the existing models up to the point where they can communicate with experimental results such as the LHC data. The difficulty is not conceptual, but rather mathematical and computational in nature. String theory is geometrical par excellence and, as such, one needs to identify the specific geometry that reduces it to the Standard Model of particle physics at low energies.

The project contributes in an essential way to the resolution of this problem. It uses experimental mathematics derived from string theory to uncover and understand new algebraic and geometric structures. The new structures feed back into string theory, providing unexpected shortcuts to incredibly hard computations. It is rare to find a new type of mathematical structure that has so much potential for problem solving. This interplay between mathematics and physics is characteristic to string theory and has crucially contributed to making it the principal driving force in fundamental particle physics.

Machine learning techniques have seen a wide range of applications in numerous areas of science and in industry. String theory and, more broadly, physics require a qualitatively different kind of machine learning, focused not only on results, but also on uncovering the mechanisms underlying them. The proposal goes beyond the standard 'black box' approach that gives correct results but no explanations by using machine lerning for the formulation of mathematically precise conjectures that can subsequently be approached using methods of algebraic geometry, everything converging towards the ultimate goal of understanding the physical implications of string theory.

String theory is a high-energy, extra-dimensional and supersymmetric theory, in which many ideas about physics beyond the Standard Model can be incorporated in a natural way. Although difficult, making contact with experimental physics is an imperative for string theory, requiring a sustained effort in developing the existing models up to the point where they can communicate with experimental results such as the LHC data. The difficulty is not conceptual, but rather mathematical and computational in nature. String theory is geometrical par excellence and, as such, one needs to identify the specific geometry that reduces it to the Standard Model of particle physics at low energies.

The project contributes in an essential way to the resolution of this problem. It uses experimental mathematics derived from string theory to uncover and understand new algebraic and geometric structures. The new structures feed back into string theory, providing unexpected shortcuts to incredibly hard computations. It is rare to find a new type of mathematical structure that has so much potential for problem solving. This interplay between mathematics and physics is characteristic to string theory and has crucially contributed to making it the principal driving force in fundamental particle physics.

Machine learning techniques have seen a wide range of applications in numerous areas of science and in industry. String theory and, more broadly, physics require a qualitatively different kind of machine learning, focused not only on results, but also on uncovering the mechanisms underlying them. The proposal goes beyond the standard 'black box' approach that gives correct results but no explanations by using machine lerning for the formulation of mathematically precise conjectures that can subsequently be approached using methods of algebraic geometry, everything converging towards the ultimate goal of understanding the physical implications of string theory.

### Planned Impact

The proposed research is fundamental in nature, being part of the quest for an ultimate theory of the universe and its mathematical foundation. This pursuit is highly regarded by the general public, having entered the collective consciousness through the impressive work of people such as Stephen Hawking. Its main virtue resides in its cultural transformative power and has significantly influenced policy and decision makers in science worldwide.

The economic impact of the programme is less immediate. On the other hand, as historical evidence proves, investment in fundamental research and in particular in mathematical physics has brought major long-term benefits for society - the effectiveness of GPS navigation, to give just one example, being unthinkable in the absence of Einstein's theory of general relativity. The timescales for this kind of foundational new knowledge in mathematics and physics can be long, in general.

Two more immediate aspects of the proposed research impact are easier to identify. The first is related to the use of machine learning for future economic development. The approach taken in the project for machine learning the mechanisms that give rise to certain patterns can be adapted for practical identification problems in economic trends. The second aspect is the direct training of young people in analytic and computational skills transferable to areas outside of academia, such as business, industry and policy making, requiring well-grounded analytical frameworks.

The research programme is linked with an important range of outreach activities including talks to local schools and the public as well as popular science publications, which will bring the fruits of the work to the wider society.

The economic impact of the programme is less immediate. On the other hand, as historical evidence proves, investment in fundamental research and in particular in mathematical physics has brought major long-term benefits for society - the effectiveness of GPS navigation, to give just one example, being unthinkable in the absence of Einstein's theory of general relativity. The timescales for this kind of foundational new knowledge in mathematics and physics can be long, in general.

Two more immediate aspects of the proposed research impact are easier to identify. The first is related to the use of machine learning for future economic development. The approach taken in the project for machine learning the mechanisms that give rise to certain patterns can be adapted for practical identification problems in economic trends. The second aspect is the direct training of young people in analytic and computational skills transferable to areas outside of academia, such as business, industry and policy making, requiring well-grounded analytical frameworks.

The research programme is linked with an important range of outreach activities including talks to local schools and the public as well as popular science publications, which will bring the fruits of the work to the wider society.

## People |
## ORCID iD |

Andrei Constantin (Principal Investigator / Fellow) |