## Physics for Machine Learning

Combining physics with machine learning is a rapidly growing field of research. Thus far, most of the work in this area focuses on leveraging recent advances in classical machine learning to solve problems that arise in the physical sciences. In this workshop, we wish to focus on a slightly less established topic, which is the converse: exploiting structures (or symmetries) of physical systems as well as insights developed in physics to construct novel machine learning methods and gain a better understanding of such methods. A particular focus will be on the synergy between the scientific problems and machine learning and incorporating structure of these problems into the machine learning methods which are used in that context. However, the scope of application of those models is not limited to problems in the physical sciences and can be applied even more broadly to standard machine learning problems, e.g. in computer vision, natural language processing or speech recognition.

Examples that fall under the theme of leveraging physics for machine learning include methods that reason from first principles, embedding fundamental laws e.g. symmetries or conservation laws in machine learning systems. Some recent work on the topic include designing equivariant neural networks to handle non-trivial geometries, designing deep neural networks as Hamiltonian systems to improve trainability, expressivity but also generalization. Many of these methods can in turn be applied to physics themselves where many fundamental laws are known to hold, vastly improving particle physics models, or molecular and fluid dynamic simulations. Additional examples which are not restricted to problems in the physical sciences include recent state-of-the-art score-based SDE diffusion models for generative modeling using insights from molecular dynamics, (recurrent) sequence models based on Hamiltonian systems or multi-particle systems and graph neural networks based on coupled oscillators or gradient flows.

The goal of this workshop is to encourage multi-disciplinary discussions and build bridges between researchers from diverse but complementary scientific backgrounds, i.e., researchers (from academia and industry) in pure machine learning as well as in the physical sciences, engineering, and applied mathematics. The workshop further aims to discuss the current state of the research field as well as possible solutions to pressing questions.

The questions this workshop aims to discuss are:

- Are there standard machine learning methods that can be interpreted and analyzed from a physics perspective? If so, what insights can we gain from that?

- What type of structures and symmetries in physical systems have not yet been leveraged?

- Are there applications of machine learning to specific types of problems in the physical sciences where only `brute-force’ approaches are applied and no structure of the problem is leveraged? If so, how can we change that?

- Which established methods developed specifically for particular scientific applications may be of interest to the broader machine learning community, e.g. neural networks parameterized as Hamiltonian systems have favorable properties such as invertibility that could be leveraged for classical machine learning approaches?

- For participants who want to focus on classical machine learning applications (i.e., no application in the physical sciences): What is a good approach to tackle problems in classical machine learning using structure from physical systems (a.k.a. a physicist’s perspective on problems in classical machine learning)?

## List of Topics

We invite all submissions on using physics for machine learning methods. A list of exemplary topics can be found below. Please note that this list is non-exhaustive. If you are not sure if your topic is suitable for the workshop, please feel free to contact any of the organizers.

- Physics-inspired machine learning; in particular for
    - Graph representation learning
    - Sequence modeling (e.g. Transformers, RNNs)
    - Generative modeling (e.g. diffusion models, score-based SDEs, normalizing flows)
    - Neural ODEs (e.g. NCDEs, CNFs)
- Equivariant neural networks
- Physics-based optimization
- Machine learning methods with a physics-based inductive bias, for instance applied to
    - Molecular simulations
    - Fluid dynamics
    - Astrophysics
    - Particle physics
    - Multi-scale problems (e.g. in multi-physics)
- Physics-based symbolic regression
- Dynamical systems reconstruction with physics-based inductive bias