Physics informed surrogate models for Bayesian Uncertainty Quantification

Abstract

In this proposal, we are interested in investigating the use of surrogate models to solve inverse problems (IP) with Bayesian uncertainty quantification (BUQ). Bayesian statistics has proved to be a coherent and adequate tool in most IPs in the presence of data and systematically quantifying the unavoidable uncertainty involved in the presence of real data. In many cases, solving IPs with BUQrequires repeated PDE solutions, making the problem impractical. We propose developing surrogate models for the PDE solutions that retain the problem s physics and yield estimates on the parameter s posterior error bounds as an alternative to this approach. We are also interested in other surrogate modeling competing methods, such as multi-fidelity, reduced order and multiphysics models, andneural networks PDE solvers. Moreover, we are interested in finding the surrogate s error bounds and how and under what circumstances these errors are correctly controlled or blurred concerning the BUQ being made and the specific goals of the problem. That is, which surrogate constructing strategy provides better results given a specific BUQ problem, possibly leading to quasi-exact results?

Document Details

Document Type
DoD Grant Award
Publication Date
Mar 08, 2024
Source ID
N629092412016

Entities

People

  • Jos Christen Gracia

Organizations

  • CIMAT Center for Mathematical Research
  • Office of Naval Research
  • United States Navy

Tags

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Fluid Dynamics (CFD)
  • Operations Research

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms