Weak Form SciML for Learning Models on Different Scales

Learn about weak form-based Scientific Machine Learning (WSciML) methods for creating and coupling mathematical models across different scales in this conference talk from IPAM's workshop on electrochemical systems. Discover how WSciML bypasses traditional physics-guided modeling approaches by enabling direct creation and inference of interpretable models from data using advanced numerical functional analysis, computational statistics, and numerical linear algebra techniques. Explore the WSINDy (equation learning) and WENDy (parameter estimation) algorithms that eliminate the need for forward-solve numerical discretizations while delivering both parsimonious mathematical models and efficient parameter estimates. Understand how these methods achieve orders of magnitude improvements in speed and accuracy compared to traditional approaches, while demonstrating superior robustness to high noise levels. Examine performance properties through canonical problems and see practical applications in plasma physics modeling, where these techniques learn models operating on different scales within a unified framework that offers compelling advantages over both conventional modeling and modern black-box neural networks.