Differentiable Foundations for Symmetry-Aware Materials Discovery: From Lie Groups to Inverse Design

The prevailing narrative in applied machine learning suggests that inductive biases are ultimately hurdles to be cleared by massive scaling. However, in the domain of physical systems, where laws are absolute and data is often expensive, incorporating symmetry as a fundamental constraint is not a limitation, it is a requirement for "indispensable utility." In this talk, I will explore the evolution of symmetry-aware architectures, shifting from invariant representations to equivariant graph neural networks (GNNs) that treat the geometric structure of 3D space as a first-class citizen.

The first part of the talk will focus on the representation of atomistic environments (point clouds). I will discuss the challenges of ensuring completeness and injectivity in these representations, touching upon formalisms like MILAD as a way to capture high-order local correlations. We will then transition to the current state-of-the-art: Euclidean symmetry-equivariant networks (E(3)NNs) developed in my group. By embedding geometric tensors and spherical harmonics directly into message-passing frameworks, these models achieve exceptional data efficiency and generalization, effectively "learning" the physics of the system rather than just the statistics of the training set.

In the second half, I will demonstrate how these equivariant frameworks enable us to move beyond forward property prediction and toward true inverse design. I will present applications in learning complex response properties—such as NMR shielding and Raman tensors—where respecting spatial and permutational symmetries is critical. Finally, I will discuss how making these workflows natively differentiable allows us to frame materials discovery as an optimization problem, utilizing generative stochastic models and "AlphaZero-style" assembly to navigate the near-infinite configurational space of crystalline and disordered materials.

I will conclude by showcasing the open-source software ecosystem (built on JAX and e3nn-jax) that our team uses to bridge the gap between abstract group theory and the practical realization of functional new materials.