Session: 13-22-01: CONCAM Distinguished Lectures on Computational Mechanics I

Paper Number: 173211

Trustworthy Neural Operator Surrogates for Multiphysics Simulations With Quantified Uncertainty - Part 2 

The field of computational mechanics is undergoing a profound transformation driven by recent advances in deep learning methodologies. A particularly promising development is the emergence of neural operators (NOs), which serve as surrogate models for physical simulations by learning mappings between infinite-dimensional function spaces, specifically, parameter-to-observation relationships governed by systems of partial differential equations (PDEs). These models offer the potential to deliver fast accurate predictions for complex multiphysics systems, enabling capabilities that were previously out of reach, including high-dimensional Bayesian inference, design optimization under uncertainty, and real-time digital twins capable of informing critical decisions in complex physical, materials, and biomedical systems. Despite their promise, the reliable deployment of neural operators remains a major open challenge. The accuracy and trustworthiness of NO-based surrogates are often compromised by multiple sources of uncertainty: the high cost and limited availability of high-fidelity simulation data for training, discrepancies between surrogate and physics models (i.e., model-form error), non-convergence during training, and, perhaps most crucially, the difficulty of selecting a suitable surrogate model for a given task or quantity of interest. 

 

The second part of the talk demonstrates the application of an iterative framework for constructing trustworthy Bayesian neural operator (BNO) surrogate models of multiphysics simulations across a range of problems, including design, inference, and real-time control in complex materials and biomedical systems. The first case involves reliability-based robust topology optimization under spatially correlated uncertainty, targeting the design of multi-material building envelope components fabricated via additive manufacturing. BNOs are trained to learn the mapping from infinite-dimensional uncertain parameters and design variables to PDE solution observables. The resulting surrogates accelerate a chance-constrained optimization formulation in a high-dimensional parameter space, enabling the design of mesoporous silica aerogel composites that provide both mechanical stability and exceptional thermal insulation. The second application employs BNO surrogates to perform PDE-constrained Bayesian inference with spatially varying parameters using imaging data. We demonstrate early-stage, patient-specific prediction of brain tumor morphology from longitudinal MRI data, capturing the biomechanical heterogeneity of tumor and brain tissues that governs tumor evolution. Finally, we present a digital twin framework for Artificial Pancreas systems, where NOs are dynamically trained on continuous glucose monitoring data from individuals with type 1 diabetes. These models predict personalized blood glucose trajectories in response to time-varying insulin inputs, meals, and physiological variations, enabling real-time, risk-averse insulin control. We conclude with a discussion of current computational challenges and future directions in scalable, rigorous methods for uncertainty quantification and validation of deep learning models in scientific computing.

Presenting Author: Danial Faghihi University at Buffalo

Presenting Author Biography: Danial Faghihi is an assistant professor in the Department of Mechanical and Aerospace Engineering at the University at Buffalo (UB), with affiliated appointments in the Department of Civil Engineering and the Institute for Artificial Intelligence and Data Science. Prior to joining UB in 2019, he was a research scientist at the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin. He earned his Ph.D. in structural engineering and mechanics from Louisiana State University. His research focuses on predictive computational modeling of complex materials and biological systems, with an emphasis on scalable uncertainty quantification frameworks at the intersection of finite element modeling, scientific machine learning, and high-performance computing. In 2022, he received the National Science Foundation CAREER Award and has authored over 40 journal articles in computational and applied mechanics. He has been organizing a series of mini symposiums on uncertainty quantification and scientific machine learning in IMECE since 2020.

Authors:

Danial Faghihi University at Buffalo