Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion

TL;DR

This paper introduces an efficient Ensemble Kalman Inversion method for Bayesian Physics Informed Neural Networks, enabling high-dimensional inverse problem inference with accurate uncertainty quantification at reduced computational cost.

Contribution

The paper proposes a novel EKI-based inference algorithm for B-PINNs, improving computational efficiency while maintaining high-quality uncertainty estimates.

Findings

Achieves inference results comparable to HMC-based B-PINNs

Reduces computational cost significantly

Provides informative uncertainty estimates in high-dimensional problems

Abstract

Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI) for high-dimensional inference tasks. We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost. These findings suggest that our proposed approach has great potential for uncertainty quantification in physics-informed machine learning for practical applications.