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math.NA2021★ 14 cited
Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs
Guang Lin, Christian Moya, Zecheng Zhang
The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of par…
math.NA2021
NH-PINN: Neural homogenization based physics-informed neural network for multiscale problems
Wing Tat Leung, Guang Lin, Zecheng Zhang
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory wh…