AL-BO: Adaptive Loss-Weighted Probabilistic Physics-Informed Neural Networks for Bayesian Optimization

Abstract Black-box optimization of expensive functions governed by physical laws remains challenging for standard Gaussian process (GP)-based Bayesian optimization (BO), which can become computationally demanding and does not naturally embed physical constraints. Existing physics-informed neural network (PINN)-based Bayesian optimization methods, hereafter termed PINN-BO methods, lack predictive uncertainty for guiding exploration, rely on fixed loss weights, and employ inefficient single-point sampling. We propose adaptive loss-weighted Bayesian optimization (AL-BO), an uncertainty-aware BO framework with a PINN surrogate that addresses all three limitations. Monte Carlo dropout (MC dropout) is incorporated to estimate epistemic uncertainty and guide acquisition. GradNorm-based adaptive loss weighting dynamically balances data fidelity and physics constraint losses during training. A lower-confidence-bound (LCB) batch acquisition strategy replaces single-point sampling to accelerate convergence. The convergence behavior and applicability of the proposed framework are discussed under the calibrated uncertainty estimates. Experiments on selected synthetic benchmarks and two chemical engineering case studies demonstrate that AL-BO achieves better optimization performance than comparable GP-BO and neural network-based baselines under the same function-evaluation budget.