article Open AccessTop 1% cited
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Computer Methods in Applied Mechanics and Engineering · 2020 · Vol. 365 · pp. 113028–113028
Ameya D. Jagtap(Brown University)Ehsan Kharazmi(Brown University)George Em Karniadakis✉(Pacific Northwest National Laboratory)
Model Reduction and Neural NetworksNeural Networks and ApplicationsFluid Dynamics and Turbulent FlowsConservation lawNonlinear systemArtificial neural networkKorteweg–de Vries equationApplied mathematicsScalar (mathematics)MathematicsInverse problemMathematical optimizationMathematical analysis
Funding
- U.S. Department of Energy
- Defense Sciences Office, DARPA
- Air Force Office of Scientific Research
Citations
1,012
FWCI
52.06
field-weighted impact
References
37
Percentile
100%
vs. same field & year
Citations per year
Cited by
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
Computer Methods in Applied Mechanics and Engineering · 2020 · 676 citations
References
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
Journal of Computational Physics · 1982 · 4,185 citations
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
IEEE Transactions on Neural Networks · 1995 · 1,113 citations
ImageNet classification with deep convolutional neural networks
Communications of the ACM · 2017 · 75,550 citations
Hidden physics models: Machine learning of nonlinear partial differential equations
Journal of Computational Physics · 2017 · 1,315 citations
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Journal of Computational Physics · 2018 · 15,047 citations
Physics-informed neural networks for high-speed flows
Computer Methods in Applied Mechanics and Engineering · 2019 · 1,145 citations
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