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Mircea Lazar of Electrical Engineering will host Professor Shukla of Brown University (USA).

Registration is required but free of charge.

Title: Blending Scientific Machine Learning and Numerical Methods: A Pathway to Next-Generation Numerical Solvers

Abstract:

Recent advancements in physics-informed neural networks (PINNs) and Deep Operator Networks (DeepONet) have significantly propelled discoveries in diverse fields such as fluid dynamics, material sciences, non-destructive evaluation, shape optimization, and subsurface imaging, among others.

In essence, PINNs embed the governing physics of underlying processes as a soft constraint within the loss function. They effectively combine multi-fidelity data鈥攏umerical, experimental, and governing equations like PDEs and ODEs鈥攖o solve forward and inverse problems within a given computational domain.

As an example, I will highlight the accuracy and efficiency of PINNs when integrated with a spectral element-based CFD solver.

In the second part of my talk, I will delve into DeepONet, which is designed to learn operators (e.g., differential, integral, Laplace) between infinite dimensional functional  spaces. I will first present its application as a CFD surrogate in a shape optimization problem. Next, I will discuss how DeepONet accelerates the Mesoscale Multi-phase Phase Field Simulator (MEMPHIS), developed by Sandia National Labs, for phase-field simulations in thin film manufacturing processes.

Bio:
Khemraj Shukla is Associate Professor of Applied Mathematics at Brown University. He held an appointment as a Research Scientist at Hewlett-Packard (HP) Labs, CA, BP America, TX and Halliburton, CO. His research focuses on the development of scalable codes on heterogeneous computing architecture for high order numerical methods. He has also worked as a Computational Scientist at University of Chicago. As a doctoral student, he developed high order numerical methods for wave propagation in a fluid  saturated porous medium under the guidance of Prof. Maarten V. de Hoop and Prof. Jesse Chan of Rice University.