Tim Wildey (Sandia National Lab)

We often seek to develop a symbiotic relationship between experimentation and simulation, where the data from the experiments informs the computational models and the computational models are used to guide the optimal acquisition of new data. In this presentation, we will discuss a few efforts at Sandia to move beyond forward simulation and build data-informed physics-based models for a variety of applications. First, we discuss recent work on optimal design and control of high-fidelity computational models for metamaterials. This involves massive-scale physics-compatible finite element discretizations for electromagnetic wave propagation and was recently awarded an R&D100 award for Meta Optics Studio in 2023. Next, we present a class of stochastic inverse problems that has been attracting increasing attention in recent years as a means to construct data-consistent physics-based computational models. Our approach, called data-consistent inversion, solves a particular class of stochastic inverse problems where a probability measure is sought on model inputs such that the corresponding push-forward measure matches a given observed, or target, measure. After briefly discussing the theoretical aspects, we address the utilization of approximate models, e.g., discretized models and surrogates (including data-driven surrogates), within this framework. Then, we describe a novel combination of this framework with Bayesian inference for digital twins and present a few practical applications. Finally, we note that the collection of experimental data can be costly and time consuming. Thus, we may only be able to afford to perform a limited number of experiments, so we must choose the experiments that are likely to produce informative data. Moreover, the optimality of the experiment must be chosen with respect to the ultimate objective. In the last part of the presentation, we present a mathematically rigorous approach for optimal experimental design for data-consistent inversion. We demonstrate that the optimal experimental design often depends on whether our objective is to characterize the uncertainty in model input parameters or in the prediction of quantities of interest that cannot be observed directly. Numerical results will be presented to illustrate both types of optimal experimental design and to highlight the differences.

Tim Wildey is the manager for the Computational Mathematics Department at Sandia National Labs. He earned his PhD from Colorado State University in 2007 on adjoint-based a posteriori error estimation for coupled multi-physics applications and held the ICES postdoctoral fellowship at the University of Texas at Austin from 2007-2010 working in the Center for Subsurface Modeling on uncertainty quantification, multi-scale discretizations and multi-level preconditioners for coupled flow and mechanics in porous media. Since joining Sandia in 2011, he has worked on error estimation for surrogate models, physics-compatible and DG discretizations, multi-scale and multi-resolution hybridizable DG methods, Bayesian and data-consistent inversion methods, optimal experimental design, extreme-scale modeling and simulation for multi-scale formulations, developing algorithms for heterogeneous computational architectures, data-compression for memory-bound applications, and uncertainty quantification for scientific machine learning. He has received several awards for his research, including a DOE Early Career Award and an R&D100 award. He is also one of the lead PIs for the CHaRMNET MMICC center funded in 2022.