Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
DOI10.1016/j.cma.2020.113028zbMath1442.92002OpenAlexW3015865829MaRDI QIDQ2184334
Ameya D. Jagtap, Ehsan Kharazmi, George Em. Karniadakis
Publication date: 28 May 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2020.113028
Artificial neural networks and deep learning (68T07) Navier-Stokes equations for incompressible viscous fluids (76D05) Neural networks for/in biological studies, artificial life and related topics (92B20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Computational methods for problems pertaining to biology (92-08)
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- Spectral and finite difference solutions of the Burgers equations
- 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
- High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
- Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Physics-informed neural networks for high-speed flows
- Method of relaxed streamline upwinding for hyperbolic conservation laws
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- 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
- Bayesian Numerical Homogenization
- Approximation by superpositions of a sigmoidal function