Bayesian physics informed neural networks for real-world nonlinear dynamical systems

DOI10.1016/j.cma.2022.115346OpenAlexW4285604295MaRDI QIDQ2679296

Xuhui Meng, Zongren Zou, A. Schäfer, Kevin Linka, George Em. Karniadakis, Ellen Kuhl

Publication date: 19 January 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.08304

zbMATH Keywords

dynamical systemsneural networksBayesian inferencemachine learningphysics-informed neural networksBayesian neural networks

Mathematics Subject Classification ID

Bayesian inference (62F15) Learning and adaptive systems in artificial intelligence (68T05) Time series analysis of dynamical systems (37M10)

Related Items (11)

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Uses Software

• PyMC
• BayesDA
• TensorFlow
• GitHub
• NUTS

Cites Work

• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• Multi-fidelity Bayesian neural networks: algorithms and applications
• Learning functional priors and posteriors from data and physics
• The reproduction number of COVID-19 and its correlation with public health interventions
• Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models
• Adversarial uncertainty quantification in physics-informed neural networks
• COVID-19 dynamics across the US: a deep learning study of human mobility and social behavior
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S
• Adaptive multiscale predictive modelling

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