Abstract

For many decades, physics-based PDEs have been commonly employed for modeling complex system responses, then traditional numerical methods were employed to solve the PDEs and provide predictions. However, when governing laws are unknown or when high degrees of heterogeneity present, these classical models may become inaccurate. In this talk we propose to use data-driven modeling which directly utilizes high-fidelity simulation and experimental measurements to learn the hidden physics and provide further predictions. In particular, we develop PDE-inspired neural operator architectures, to learn the mapping between loading conditions and the corresponding system response. By parameterizing the increment between layers as an integral operator, our neural operator can be seen as the analog of a time-dependent nonlocal equation, which captures the long-range dependencies in the feature space and is guaranteed to be resolution-independent. Moreover, when applying to (hidden) PDE solving tasks, our neural operator provides a universal approximator to a fixed point iterative procedure, and partial physical knowledge can be incorporated to further improve the model’s generalizability and transferability. As an application, we learn the material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and show that the learnt model substantially outperforms conventional constitutive models.

Short bio

Yue Yu received her B.S. from Peking University in 2008, and her Ph.D. from Brown University in 2014. She was a postdoc fellow at Harvard University after graduation, and then she joined Lehigh University as an assistant professor of applied mathematics and was promoted to associate professor in 2019. Her research lies in the area of applied and computational mathematics, with recent projects focusing on nonlocal problems and scientific machine learning. She has received an NSF Early Career award and an AFOSR Young Investigator Program (YIP) award.