Bayesian PINNs for elliptic PDEs have posteriors that contract around the true solution at near-optimal rates, with the prior adapting automatically to unknown smoothness.
Posterior contraction for sparse neural networks in besov spaces with intrinsic dimensionality.arXiv preprint arXiv:2506.19144
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POTTERS extends the Potts model with generalized spatial dependence and external priors for Bayesian remote sensing image segmentation via variational inference, without needing target-region labels.
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Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
Bayesian PINNs for elliptic PDEs have posteriors that contract around the true solution at near-optimal rates, with the prior adapting automatically to unknown smoothness.
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Scalable Bayesian Spatial Mixture Modelling for Remote Sensing Image Segmentation
POTTERS extends the Potts model with generalized spatial dependence and external priors for Bayesian remote sensing image segmentation via variational inference, without needing target-region labels.