Learning functional priors and posteriors from data and physics

DOI10.1016/j.jcp.2022.111073OpenAlexW3167256391MaRDI QIDQ2135824

Yanyan Li

Publication date: 9 May 2022

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

Full work available at URL: https://arxiv.org/abs/2106.05863

zbMATH Keywords

uncertainty quantificationmeta-learningphysics-informed neural networksoperator regressionGANsfunctional priors

Mathematics Subject Classification ID

Statistics (62-XX) Artificial intelligence (68Txx) Approximations and expansions (41Axx)

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Uses Software

• NUTS
• Wasserstein GAN
• DeepONet
• tfp.mcmc

Cites Work

• Unnamed Item
• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• Machine learning of linear differential equations using Gaussian processes
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• Multi-fidelity Bayesian neural networks: algorithms and applications
• Physics-informed semantic inpainting: application to geostatistical modeling
• DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
• A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• GAN-Based Priors for Quantifying Uncertainty in Supervised Learning
• Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
• Advanced Lectures on Machine Learning