Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion
This work addresses the problem of computational inefficiency in uncertainty quantification for physics-informed machine learning, offering a more practical solution for inverse problems in fields like engineering and science, though it is incremental as it builds on existing B-PINN frameworks.
The paper tackles the computational challenge of high-dimensional posterior inference in Bayesian Physics Informed Neural Networks (B-PINNs) by proposing an efficient algorithm using Ensemble Kalman Inversion (EKI), achieving inference results with uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based methods at a much reduced computational cost.
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.