Preprint
Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion
ArXiv.org
03/13/2023
DOI: 10.48550/arxiv.2303.07392
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.
Details
- Title: Subtitle
- Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion
- Creators
- Andrew PensoneaultXueyu Zhu
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2303.07392
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 03/13/2023
- Academic Unit
- IIHR--Hydroscience and Engineering; Mathematics
- Record Identifier
- 9984378329702771
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