Past Event: Oden Institute Seminar

Joint ASE/Oden Institute Seminar: Foundations of Data-Efficient and Uncertainty-Aware Scientific Machine Learning

Nicholas Nelsen, Ph.D Candidate, Mechanical Engineering and Applied & Computational Mathematics, California Institute of Technology

Abstract

Scientific machine learning (SciML) blends modern ideas from artificial intelligence with more traditional scientific computing paradigms. It promises to accelerate model-driven tasks with fast surrogates and discover physical laws directly from experimental data. This talk introduces a SciML framework that is specifically tailored to the continuum structure of scientific data; samples of such data include the spatiotemporal fields that solve partial differential equations. The framework enables the design of scalable new learning algorithms for complex physical systems arising in engineering problems and the ability to quantify the inherent uncertainties in these algorithms. The talk reviews rigorous theoretical guarantees on the reliability and trustworthiness of the proposed methods in the presence of data discretization and noise. The error and convergence analysis also uncovers novel insights into the subtle interplay between the underlying problem structure and the amount of training data required to learn an accurate model. Numerical results for fluid flow, materials science, climate modeling, and medical imaging problems demonstrate the practical utility of the proposed SciML methodology