Multi-variance replica exchange stochastic gradient MCMC for inverse and forward Bayesian physics-informed neural network

Understand

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems.

• However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem.
• In this work, we propose a multi-variance replica exchange stochastic gradient Langevin diffusion method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem.
• Replica exchange methods are capable of escaping from the local traps and accelerating the convergence.