PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks

Black-box optimization has emerged as an effective technique in many real-world applications to find the global optimum of expensive, noisy black-box functions. Some notable applications include hyper-parameter optimization in machine learning algorithms Snoek et al. [2012], Bergstra and Bengio [2012], synthesis of short polymer fiber materials, alloy design, 3D bio-printing, and molecule design Greenhill et al. [2020], Shahriari et al. [2015], optimizing design parameters in computational fluid dynamics Morita et al. [2022], and scientific research (e.g., multilayer nanoparticle, photonic crystal topology) Kim et al. [2022]. Bayesian Optimization is a popular example of black-box optimization method. Typically, Bayesian Optimization algorithms use a probabilistic regression model, such as a Gaussian Process (GP), trained on existing function observations. This model is then utilized to create an acquisition function that balances exploration and exploitation to recommend the next evaluation point for the black-box functions. Various options exist for acquisition functions, including improvement-based methods like Probability of Improvement Kushner [1964], Expected Improvement Mockus et al. [1978], the Upper Confidence Bound Srinivas