Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations

DOI10.1016/j.jcp.2021.110364OpenAlexW3023243091MaRDI QIDQ2124408

Andrew P. King, Christopher J. Arthurs

Publication date: 11 April 2022

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

Full work available at URL: https://arxiv.org/abs/2005.05092

zbMATH Keywords

trainingactive learningNavier-Stokesdeep learningcomputing methods

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Artificial intelligence (68Txx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Related Items (4)

Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Improved deep neural networks with domain decomposition in solving partial differential equations ⋮ Error assessment of an adaptive finite elements -- neural networks method for an elliptic parametric PDE ⋮ A physics-informed learning approach to Bernoulli-type free boundary problems

Uses Software

• Gmsh
• SciPy
• Nektar++
• Python
• TensorFlow

Cites Work

• Efficient simulation of cardiac electrical propagation using high-order finite elements. II: Adaptive \(p\)-version
• Efficient simulation of cardiac electrical propagation using high order finite elements
• Nektar++: an open-source spectral/\(hp\) element framework
• Inferring solutions of differential equations using noisy multi-fidelity data
• Machine learning of linear differential equations using Gaussian processes
• Hidden physics models: machine learning of nonlinear partial differential equations
• Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

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