Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)
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Abstract (arXiv)
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the expected NN output, as well as its weights. Also, as we can have access to the posterior probability distributions, naturally uncertainties can be quantified. Also, variational inference and Monte Carlo dropout are employed to provide predictive means and variances for reconstructed images. Un example of applications to deconvolution and super-resolution is considered, details of the different steps of implementations are given, and some preliminary results are presented.
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References · 7
- 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
- 2015Weight Uncertainty in Neural Networkscited by 554
- 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
- 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
- 2019Functional Variational Bayesian Neural Networkscited by 127
- 2023Tractable Function-Space Variational Inference in Bayesian Neural Networkscited by 41
- 2018Deep learning electromagnetic inversion with convolutional neural networkscited by 12
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