Defining Foundation Models for Computational Science - Toward Clarity and Rigor

Explore the emerging field of foundation models in computational science through this comprehensive seminar that addresses the critical need for rigorous definitions and standards in this rapidly evolving domain. Examine how foundation models, which have already transformed natural language processing and computer vision, are now making their way into scientific computing applications including fluid dynamics, materials design, and climate modeling. Learn about the essential characteristics that define foundation models in computational science, with emphasis on principles such as generalization, reusability, and scalability that distinguish them from traditional machine learning approaches. Discover the Data-Driven Finite Element Method (DD-FEM) as a concrete implementation pathway that combines the mathematical rigor of classical numerical methods with the adaptability of modern machine learning techniques. Understand the challenges of establishing community-wide standards for evaluating and developing foundation models in high-consequence scientific domains where accuracy and reliability are paramount. Gain insights into the speaker's pioneering work on reduced-order models, machine learning-based nonlinear manifolds, space-time ROMs, and latent space dynamics identification that accelerate time-critical simulations in inverse problems, design optimization, and uncertainty quantification. Engage with open questions and collaboration opportunities as the computational science community works to establish what foundation models should mean for scientific applications, moving beyond buzzwords toward rigorous scientific concepts that can drive meaningful advances in computational research.