PI-CoF: A Bilevel Optimization Framework for Solving Active Learning Problems using Physics-Information
Year: 2024
Type: conference-paper
Abstract: We propose a broadly applicable method for incorporating physics information into existing machine learning (ML) models of any type. The proposed method - we refer as PI-CoF for Physics-Informed Correction Factors - introduces correction factors for pointwise inference, which are determined by solving a regularized unconstrained optimization problem for reconciliation of physics information and ML model predictions. Regularization is introduced to prevent excessive use of corrections, while individually weighted costs are employed to adjust corrections based on the level of prediction uncertainty, allowing stronger corrections for predictions with higher uncertainty and weaker corrections for those with lower uncertainty. When ML models are used in an optimization context, using the proposed approach translates into a bilevel optimization problem, where the reconciliation problem is solved as an inner problem each time before evaluating the objective and constraint functions of the outer problem. The utility of the proposed approach is demonstrated through a numerical example, emphasizing constraint satisfaction in a safe Bayesian optimization (BO) setting. Furthermore, a simulation study is carried out by using PI-CoF for the real-time optimization of a fuel cell system. The results show reduced fuel consumption and better reference tracking performance when using the proposed PI-CoF approach in comparison to a constrained BO algorithm that does not incorporate physics information.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Marie Curie
OpenAlex ID: W4402437067