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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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.