Ziming Liu
Affiliation
MIT
Talk Title
Learning conserved quantities from data and equations
Abstract
Conserved quantities play a crucial role not only in revealing symmetries but also in enabling system reductions, thereby simplifying computations. However, deriving conservation laws manually is often tedious and constrained by human intuition and symbolic guesswork. To address this challenge, I will introduce our AI Poincaré models, which are capable of discovering conserved quantities directly from data and differential equations. Notably, I will illustrate how the task of learning conservation laws can be reframed as a geometric problem. Our model not only rediscovers many well-known conserved quantities but has also uncovered a novel conserved quantity in atmospheric chemistry—subsequently verified and generalized by domain experts—thus completing the discovery loop.
Bio
Ziming Liu is a PhD candidate at the Massachusetts Institute of Technology, advised by Max Tegmark. With a strong background in both AI and physics, he is uniquely positioned to explore the foundations of AI from a scientific perspective. His research spans both Science for AI—leveraging scientific insights to understand and develop AI models—and AI for Science—using AI to accelerate scientific discovery. His work has garnered significant attention within the community, including contributions to Kolmogorov-Arnold Networks, Poisson flow generative models, and the demystification of grokking.