Dr. Yue Yu

Professor of Applied Mathematics

Lehigh University

Topic: "Synergizing Imperfect Physics Knowledge and Measurements with Neural Operators"

Abstract:
Over the past several decades, constitutive models within PDE-based continuum mechanics have been commonly employed to characterize material response from experimental measurements. Typically, a strain energy density function is predefined with a specific functional form. Then, the material parameters are calibrated through an inverse method or analytical stress--strain fitting to test data. However, in this approach accuracy and computational feasibility can be compromised when the physics knowledge is limited, e.g., when the governing law remains unknown. On the other hand, machine learning (ML) based approaches have emerged to provide more flexible predictive models. However, the pure data-driven approaches generally do not guarantee fundamental physical laws. As a result, their performances highly rely on the quantity and coverage of available data.
In this talk, we develop physics-guided neural network models to mitigate the above challenges in pure physics-based and data-driven approaches. The key idea is to encode partial physical laws and PDE solving techniques through neural network architecture design. As such, the learnt model automatically preserves fundamental physical laws while still being readily applicable to learn physical systems directly from experimental measurements. To this end, we employ nonlocal neural operators, which learn a surrogate mapping between function spaces and act as implicit solution operators of hidden governing PDE equations. We showcase the proposed physics-guided neural operators in preserving objectivity, momentum balance laws, and conservation laws. This feature substantially enhances the model's generalizability and reliability, especially in small and noisy data regimes. To illustrate the real-world applicability of our approach, we demonstrate the direct learning and monitoring of material models from digital image correlation (DIC) displacement tracking measurements on porcine tricuspid valve leaflet tissues, showing the superior performance of the learned model when compared to traditional constitutive models.

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 full professor in 2023. Her research lies in the area of applied mathematics and computational mechanics, 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.

Thursday, April 11, 2024

102 BEH

11:00am

Host: Hessam Babaee