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

arXiv: https://arxiv.org/abs/2402.03243 · HTML: https://mlsanity.com/paper/2402.03243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Solving and Learning Nonlinear PDEs with Gaussian Processes](https://mlsanity.com/paper/2103.12959/) (2021)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)

## 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.