Physics-Informed Machine Learning for Uncertainty Quantification and Optimization

Abstract

The purpose of uncertainty quantification in the system response prediction is to support decision-making under uncertainty. For complex engineering systems, recent efforts have focused on using computational models for optimizing the process parameters and analyzing the response of an engineering system for a variety of input realizations, since conducting experiments to directly measure the true response for many input realizations is often not affordable. The use of physics-based or ML models instead of experiments would be more economical than using an experiment-based trial-and-error approach in exploring a wide range of process parameter settings and their effects on the product quality. However, for complex phenomena, physics-based models can be computationally expensive and affected by model errors. Therefore, this research investigates the combination of physics-based models and experimental data to build effective models for optimization under uncertainty that reduce computational effort while maintaining accuracy. Towards this end, four individual objectives are pursued: (1) Machine learning using both physics knowledge and experimental data, (2) Adaptive surrogate modeling with high-dimensional spatio-temporal output, (3) Multi-level information fusion for model calibration, and (4) Decision-making under uncertainty. First, several physics-informed machine learning (PIML) strategies are developed and investigated for bond quality and porosity predictions of additively manufactured specimens (namely, fused filament fabrication (FFF)) using physics constraints, physics-based models, and experimental data. Next, an efficient surrogate modeling technique is developed for high-dimensional time-dependent systems with spatio-temporal output and demonstrated for a gas turbine engine. Since 3D finite element models for thermo-mechanical systems are computationally expensive, we develop an adaptive sampling strategy that is aimed at optimizing the computational resource allocation by considering both the physics information and exploration of the entire design space to improve the model performance within the available resources. Next, we develop a multi-level Bayesian calibration approach, where an iterative strategy is developed for information fusion from heterogeneous sources to estimate the global and local model parameters with asynchronous real-time monitoring data. Finally, we develop a methodology for decision-making under uncertainty using the ML models for FFF process parameter design, to satisfy multiple quality criteria such as porosity and geometric accuracy.