Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion. (arXiv:2303.07392v1 [stat.ML])

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.