Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)
This work addresses uncertainty-aware image reconstruction for applications like deconvolution and super-resolution, but it appears incremental as it extends existing PINN methods with Bayesian techniques.
The paper tackles uncertainty quantification in linear inverse problems by developing a hierarchical Bayesian formulation of PINNs, called BPINN-IP, which incorporates prior knowledge on neural network outputs and weights, and applies it to deconvolution and super-resolution with preliminary results.
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.