MAE Colloquium: Nicholas Nelsen Ph.D.

Description

Title: Foundations of Data-Efficient and Uncertainty-Aware Scientific Machine Learning

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, such as 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 noisy observations. The error analysis also uncovers useful 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, solid mechanics, climate modeling, and medical imaging problems demonstrate the practical utility of the proposed SciML methodology.

Bio: Nicholas Nelsen is a final year Ph.D. candidate at Caltech. He has research interests in high-dimensional problems at the intersection of statistics and computational science and engineering. In particular, he works on the theory and design of reliable and trustworthy learning algorithms that enable scientific computation and discovery. Nicholas received a SIAM Review SIGEST award for his work on operator learning; this work was also recognized as a spotlight at the NeurIPS machine learning conference. His research is supported by an Amazon AI4Science Fellowship and an NSF Graduate Research Fellowship. Nicholas obtained a M.Sc. from Caltech in 2020 and a B.Sc. in Mathematics, B.S.M.E., and B.S.A.E. from Oklahoma State University in 2018.