B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while...

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Bibliographic Details
Published in:Journal of computational physics 2021-01, Vol.425 (C), p.109913, Article 109913
Main Authors: Yang, Liu, Meng, Xuhui, Karniadakis, George Em
Format: Article
Language:English
Subjects:
Artificial neural networks
Bayesian analysis
Bayesian physics-informed neural networks
Computational physics
Hamiltonian Monte Carlo
Neural networks
Noise prediction
Noisy data
Nonlinear PDEs
Partial differential equations
Uncertainty
Variational inference
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