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.
sup f∈F 1 n nX i=1 f(X i) # + √2vnt n + U t 3n , where vn = 2UE
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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.