Discovery of Hidden Symmetries and Conservation Laws using Physics-Aware Machine Learning

Organization: ML4SCI

Mentors: Diptarko Choudhury (NISER), Sergei Gleyzer (University of Alabama), Ruchi Chudasama (University of Alabama), Samuel Campbell (University of Alabama), Emanuele Usai (University of Alabama), Alex Roman (University of Alabama)

Abstract: This project addresses the challenge of discovering hidden symmetries in physics datasets using machine learning. This is a crucial step towards building more robust, data-efficient, and interpretable physics-aware models. Symmetries fundamental to physics (like those in the Standard Model) can become obscured in complex data representations. This project developed and benchmarked ML techniques, inspired by recent literature, to first uncover rotational symmetry in a controlled MNIST environment (using VAE and MLP analysis) and then extended these methods to probe symmetries within high-energy physics contexts, potentially utilizing CMS open data. The project aimed to implement unsupervised discovery algorithms, evaluate their effectiveness, and explore the use of discovered symmetries in constructing physics-aware models, aligning with the goals of advancing ML applications in scientific domains.

Motivation & Background

Physics is deeply intertwined with the study of symmetry, linking invariance principles to fundamental conservation laws. While symmetries are often clear in standard formalisms (like 4-vectors), they can become "hidden" in complex, high-dimensional data representations common in experimental physics or abstract feature spaces learned by ML models. Automating the discovery of these hidden symmetries is a key challenge and opportunity at the intersection of physics and machine learning. Recent progress in unsupervised and physics-aware ML provides powerful tools for this task. Successfully learning these symmetries enables the construction of models that inherently respect physical constraints, leading to improved performance and generalization.

Project Goals & Deliverables

• Foundational Latent Space: Prepare rotated MNIST dataset and train a VAE baseline.
• Supervised Symmetry Characterization: Implement and train an MLP on the VAE's latent space to learn transformations.
• Unsupervised Symmetry Discovery: Explore and implement unsupervised techniques (e.g., learning Lie algebra generators, GANS, or PDE minimization) to discover rotational symmetry in MNIST latent space without explicit angle labels.
• Extension to Physics Use Case: Adapt and apply discovery techniques to a complex physics dataset (e.g., CMS open data).
• Physics-Aware Model & Benchmarking: Utilize discovered symmetries to inform the design of a simple physics-aware model and benchmark it.

Technologies Used: Python, PyTorch, TensorFlow, Variational Autoencoders (VAEs), Multilayer Perceptrons (MLPs), Generative Adversarial Networks (GANs), Physics-Informed Machine Learning techniques.

For more details, you can view the full project proposal.