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

Paper Number: 173210

Trustworthy Neural Operator Surrogates for Multiphysics Simulations With Quantified Uncertainty - Part 1 

Abstract (Part 1):

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 first part of this talk introduces a unified framework for constructing trustworthy NO surrogates through the lens of uncertainty quantification (UQ). We begin by representing model-form uncertainty using a posteriori error estimation between NO predictions and PDE solutions. We then present a scalable Bayesian training algorithm that leverages the model-form uncertainty representation and Newton-based optimization to efficiently infer the probability distribution of high-dimensional weight parameters within NOs. Finally, we outline an iterative framework that integrates model plausibility, goal-oriented design of training data, and validation under uncertainty methodologies. This approach systematically identifies the most reliable NO surrogate for a specific quantity of interest across a broad model space that encompasses various architectures, and hyperparameters.
 

References:

[1] Singh, P. K., Maupin, K., Faghihi, D. (2024). A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty. Computer Methods in Applied Mechanics and Engineering, 427, pp.117061. DOI 

[2] Tan, J., Faghihi, D. (2024). A Scalable Algorithm for PDE-constrained Design of Thermal Insulation Components Under Uncertainty. Computer Methods in Applied Mechanics and Engineering, 419, pp.116628. DOI 

[3] Liang, B., Tan, J., Lozenski, L., Hormuth, D.A., Yankeelov, T.E., Villa, U., Faghihi, D. (2023). Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth. IEEE Transactions on Medical Imaging, 42(10), pp.2865-2875. DOI 

[4] Tan, J., Liang, B., Singh, P. K., Maupin, K., Faghihi, D. (2022). Toward Selecting Optimal Predictive Multiscale Models. Computer Methods in Applied Mechanics and Engineering, 402, pp. 115517. DOI 

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