David Bortz - Weak form SciML for Learning Models on Different Scales - IPAM at UCLA
Recorded 07 October 2025. David Bortz of the University of Colorado, Boulder, presents "Weak form SciML for Learning Models on Different Scales" at IPAM's Bridging Scales from Atomistic to Continuum in Electrochemical Systems Workshop.Abstract: The creation and coupling of mathematical models on different scales is central to modern scientific discovery. As more realism is demanded of models, however, the conventional framework of physics-guided model proposal, parameter fitting, and multiscale validation and refinement becomes unwieldy, expensive, and computationally daunting. Recent advances in Weak form-based Scientific Machine Learning (WSciML) allow for the creation and inference of interpretable models directly from data via advanced numerical functional analysis, computational statistics, and numerical linear algebra techniques. This class of methods completely bypasses the need for forward-solve numerical discretizations and yields both parsimonious mathematical models and efficient parameter estimates. These methods are orders of magnitude faster and more accurate than traditional approaches and far more robust to the high noise levels. The combination of these features in a single framework provides a compelling alternative to both traditional modeling approaches as well as modern black-box neural networks. In this talk, I will present our weak form approach, describing our equation learning (WSINDy) and parameter estimation (WENDy) algorithms. I will discuss their performance properties on several canonical problems and demonstrate how they can be used to learn models on different scales for a problem in plasma physics.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-bridging-scales-from-atomistic-to-continuum-in-electrochemical-systems/ Receive SMS online on sms24.me
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