Colloquium-Physics Department - William Gilpin, Assistant Professor (UT Austin)

Geometry guides generalization in zero-shot learning of dynamical systems What limits our ability to model multiscale systems, like turbulent flows or biological dynamics? Classical scientific machine learning uses inductive biases to encode domain knowledge into data-driven models. Yet recent efforts to build scientific foundation models suggest that scale alone unlocks surprising generalization capabilities. I will describe my group’s efforts to understand generalization in scientific machine learning. We pretrain a foundation model on hundreds of thousands of dynamical systems, and discover that it develops the ability to zero-shot forecast unseen systems without retraining. Using mechanistic interpretability probes, we find that generalization capability in large models is enabled by a complex set of internal mechanisms, including zero-shot transfer across scales, in-context learning of transfer operators, and a neural scaling law relating performance to the diversity of dynamical