B-DeepONet: an enhanced Bayesian deeponet for solving noisy parametric PDEs using accelerated replica exchange SGLD

DOI10.1016/j.jcp.2022.111713OpenAlexW4307570062MaRDI QIDQ2106911

Guang Lin, Zecheng Zhang, Christian Moya

Publication date: 29 November 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2022.111713

zbMATH Keywords

noisy dataBayesian methodreplica exchangeLangevin diffusiondeep operator networkparametric PDE

Mathematics Subject Classification ID

Miscellaneous topics in partial differential equations (35Rxx) Parabolic equations and parabolic systems (35Kxx) Probabilistic methods, stochastic differential equations (65Cxx)

Related Items (2)

Reliable extrapolation of deep neural operators informed by physics or sparse observations ⋮ Multi-agent reinforcement learning aided sampling algorithms for a class of multiscale inverse problems

Uses Software

• DeepONet

Cites Work

• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
• Laplace's method revisited: Weak convergence of probability measures
• A multi-stage deep learning based algorithm for multiscale model reduction
• Computational multiscale methods for quasi-gas dynamic equations
• DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• Diffusion for Global Optimization in $\mathbb{R}^n $
• Solving parametric PDE problems with artificial neural networks

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