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

arXiv 2402.03243 ↗First posted 5 Feb 2024cs.LGcited by 0

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Abstract (arXiv)

Black-box optimization is a powerful approach for discovering global optima in noisy and expensive black-box functions, a problem widely encountered in real-world scenarios. Recently, there has been a growing interest in leveraging domain knowledge to enhance the efficacy of machine learning methods. Partial Differential Equations (PDEs) often provide an effective means for elucidating the fundamental principles governing the black-box functions. In this paper, we propose PINN-BO, a black-box optimization algorithm employing Physics-Informed Neural Networks that integrates the knowledge from Partial Differential Equations (PDEs) to improve the sample efficiency of the optimization. We analyze the theoretical behavior of our algorithm in terms of regret bound using advances in NTK theory and prove that the use of the PDE alongside the black-box function evaluations, PINN-BO leads to a tighter regret bound. We perform several experiments on a variety of optimization tasks and show that our algorithm is more sample-efficient compared to existing methods.

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References · 14

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  2. 2017On Kernelized Multi-armed Banditscited by 348
  3. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  4. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  5. 2017Max-value Entropy Search for Efficient Bayesian Optimizationcited by 202
  6. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
  7. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 128
  8. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  9. 2017Bayesian Optimization with Gradientscited by 59
  10. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
  11. 2020A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challengescited by 51
  12. 2017Linearly constrained Gaussian processescited by 41
2 more
  1. 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
  2. 2021Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structurecited by 15

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