Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

An adaptive Hessian approximated stochastic gradient MCMC method

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Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications

(2021) Yating Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

(2021) Sifan Wang et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

(2020) Liu Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Diffusion Equation-Assisted Markov Chain Monte Carlo Methods for the Inverse Radiative Transfer Equation

(2019) Qin Li et al.   Entropy

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

(2015) Weixuan Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Inverse problems: A Bayesian perspective

(2010) A. M. Stuart   ACTA NUMERICA