PI-CoF: A Bilevel Optimization Framework for Solving Active Learning Problems using Physics-Information
CoRR(2024)
摘要
Physics informed neural networks (PINNs) have recently been proposed as
surrogate models for solving process optimization problems. However, in an
active learning setting collecting enough data for reliably training PINNs
poses a challenge. This study proposes a broadly applicable method for
incorporating physics information into existing machine learning (ML) models of
any type. The proposed method - referred to as PI-CoF for Physics-Informed
Correction Factors - introduces additive or multiplicative correction factors
for pointwise inference, which are identified by solving a regularized
unconstrained optimization problem for reconciliation of physics information
and ML model predictions. 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 not using physics
information.
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