Mathematical Sciences Department
Harold J. Gay Lecture
Title: Agentic Scientific Machine Learning
Speaker: Prof. George Karniadakis
Abstract: Scientific Machine Learning (SciML) integrates data-driven inference with physical modeling to solve complex problems in science and engineering. However, the design of SciML architectures, loss formulations, and training strategies remains an expert-driven research process, requiring extensive experimentation and problem-specific insights. We introduce ATHENA, a collaborative multi-agent system in which about 20 specialized AI agents collaborate to propose, critique, and refine SciML solutions through structured reasoning and iterative evolution. The framework integrates structured debate, retrieval-augmented method memory, and ensemble-guided evolutionary search, enabling the agents to generate and assess new hypotheses about architectures and optimization procedures. Across physics-informed learning and operator learning tasks, the framework discovers solution methods that outperform single agent and human-designed baselines by orders of magnitude in error reduction. The agents produce novel strategies -- including adaptive mixture-of-expert architectures, decomposition based PINNs, and physics-informed operator learning models -- that do not appear explicitly in the curated knowledge base. They also prove error estimates, universal approximation theorems, and discover singularities in PDEs. These results show that collaborative reasoning among AI agents can yield emergent methodological innovation, suggesting a path toward scalable, transparent, and autonomous discovery in scientific computing.