Title: Towards Physics-Based Modeling from Heterogeneous Data: Multiresolution Multifidelity Neural Operators
Abstract: Learning the action of a mechanistic operator (e.g., governed by a partial differential equation) from data is challenging when observations are collected at different spatiotemporal resolutions, fidelities, and modalities. In many practical settings, data are irregular, incomplete, and heterogeneous, yet integrating such information can significantly improve predictive accuracy while reducing data and computational costs. In this talk, I will present a multiresolution and multifidelity neural operator framework that enable learning directly from heterogeneous datasets defined on meshes and point clouds with varying discretizations. By integrating classical ideas from function approximation into neural operators, the proposed approach achieves resolution independence and provides built-in error indicators. I will also demonstrate how combining inexpensive low-fidelity simulations with limited high-fidelity experimental data leads to more efficient and reliable model identification, with applications to microstructure-dependent material modeling.
Speaker Bio: Dr. Bahador Bahmani is a tenure-track Assistant Professor in the Department of Mechanical Engineering at Northwestern University. His research lies at the intersection of computational solid mechanics, scientific machine learning, and uncertainty quantification, aiming to enable autonomous and scalable modeling of inelastic, multiscale materials and structures. Prior to this, he was a Postdoctoral Research Fellow at the Hopkins Extreme Materials Institute at Johns Hopkins University. He received his Ph.D. in Engineering Mechanics from Columbia University in 2024.
