article Open AccessTop 1% cited
Hidden physics models: Machine learning of nonlinear partial differential equations
Journal of Computational Physics · 2017 · Vol. 357 · pp. 125–141
Maziar Raissi✉(Brown University)George Em Karniadakis(Brown University)
Model Reduction and Neural NetworksGaussian Processes and Bayesian InferenceNeural Networks and ApplicationsNonlinear systemPartial differential equationComputer scienceDynamical systems theoryInferenceDifferential equationMathematicsApplied mathematicsArtificial intelligencePhysics
Funding
- Defense Advanced Research Projects Agency
- Multidisciplinary University Research Initiative
- Air Force Office of Scientific Research
- Army Research Office
Citations
1,315
FWCI
54.86
field-weighted impact
References
88
Percentile
100%
vs. same field & year
Citations per year
Cited by
Physics-informed neural networks for high-speed flows
Computer Methods in Applied Mechanics and Engineering · 2019 · 1,145 citations
Explainable Machine Learning for Scientific Insights and Discoveries
IEEE Access · 2020 · 937 citations
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 · 1,012 citations
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
Computer Methods in Applied Mechanics and Engineering · 2020 · 676 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
Modal Analysis of Fluid Flows: Applications and Outlook
AIAA Journal · 2019 · 598 citations
References
Theory of reproducing kernels
Transactions of the American Mathematical Society · 1950 · 5,387 citations
Regression Shrinkage and Selection Via the Lasso
Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1996 · 50,746 citations
Networks for approximation and learning
Proceedings of the IEEE · 1990 · 3,267 citations
Solutions of Ill-Posed Problems.
Mathematics of Computation · 1978 · 8,191 citations
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Proceedings of the National Academy of Sciences · 2016 · 4,342 citations
Data-driven discovery of partial differential equations
Science Advances · 2017 · 1,500 citations
Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Journal of the American Statistical Association · 2003 · 4,326 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.