article Open AccessTop 1% cited
DGM: A deep learning algorithm for solving partial differential equations
Journal of Computational Physics · 2018 · Vol. 375 · pp. 1339–1364
Justin Sirignano✉(University of Illinois Urbana-Champaign)Konstantinos Spiliopoulos(Boston University)
Model Reduction and Neural NetworksGenerative Adversarial Networks and Image SynthesisMeteorological Phenomena and SimulationsPartial differential equationMathematicsArtificial neural networkGalerkin methodPolygon meshAlgorithmBoundary (topology)Basis functionBoundary value problemApplied mathematics
Funding
- National Science Foundation
Citations
2,058
FWCI
93.98
field-weighted impact
References
65
Percentile
100%
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Citations per year
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References
Approximation capabilities of multilayer feedforward networks
Neural Networks · 1991 · 5,992 citations
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
Neural Networks · 1990 · 2,101 citations
Long Short-Term Memory
Neural Computation · 1997 · 95,078 citations
Valuing American Options by Simulation: A Simple Least-Squares Approach
Review of Financial Studies · 2001 · 3,289 citations
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks · 1998 · 2,128 citations
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Journal of Fluid Mechanics · 2016 · 1,537 citations
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