See https://arxiv.org/pdf/2006.04228.pdf as a guiding document. We can essentially have the NNBayesianPDE which is the same as the other but spits out a Bayesian estimation problem a la https://turing.ml/dev/tutorials/3-bayesnn/ with ADVI and use that to train with uncertainties. This would be a great GSoC project.
See https://arxiv.org/pdf/2006.04228.pdf as a guiding document. We can essentially have the NNBayesianPDE which is the same as the other but spits out a Bayesian estimation problem a la https://turing.ml/dev/tutorials/3-bayesnn/ with ADVI and use that to train with uncertainties. This would be a great GSoC project.