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Improvement of Bayesian PINN Training Convergence in Solving Multi-scale PDEs with Noise

Improvement of Bayesian PINN Training Convergence in Solving Multi-scale PDEs with Noise

Bayesian Physics Informed Neural Networks (BPINN) have received considerable attention for inferring differential equations' system states and physical parameters according to noisy observations. However, in practice, Hamiltonian Monte Carlo (HMC) used to estimate the internal parameters of BPINN often encounters troubles, including poor performance and awful convergence for a given …