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Numerical Methods for Ordinary Differential Equations
Numerical Methods for Ordinary Differential Equations
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Numerical Methods for Ordinary Differential Equations

Butcher, J. C

Newark: John Wiley & Sons, Incorporated 2016

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Solving high-dimensional partial differential equations using deep learning
Solving high-dimensional partial differential equations using deep learning
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Solving high-dimensional partial differential equations using deep learning

Han, Jiequn ; Jentzen, Arnulf ; E, Weinan

Proceedings of the National Academy of Sciences - PNAS, 2018-08, Vol.115 (34), p.8505-8510 [Periódico revisado por pares]

United States: National Academy of Sciences

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3
DGM: A deep learning algorithm for solving partial differential equations
DGM: A deep learning algorithm for solving partial differential equations
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DGM: A deep learning algorithm for solving partial differential equations

Sirignano, Justin ; Spiliopoulos, Konstantinos

Journal of computational physics, 2018-12, Vol.375, p.1339-1364 [Periódico revisado por pares]

Cambridge: Elsevier Inc

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Differential-Algebraic Equations: A Projector Based Analysis
Differential-Algebraic Equations: A Projector Based Analysis
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Differential-Algebraic Equations: A Projector Based Analysis

Lamour, René ; März, Roswitha ; Tischendorf, Caren

Berlin, Heidelberg: Springer-Verlag 2013

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5
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

Jagtap, Ameya D. ; Kawaguchi, Kenji ; Karniadakis, George Em

Journal of computational physics, 2020-03, Vol.404 (C), p.109136, Article 109136 [Periódico revisado por pares]

Cambridge: Elsevier Inc

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6
Nonlinear Model Reduction via Discrete Empirical Interpolation
Nonlinear Model Reduction via Discrete Empirical Interpolation
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Nonlinear Model Reduction via Discrete Empirical Interpolation

Chaturantabut, Saifon ; Sorensen, Danny C

SIAM journal on scientific computing, 2010-01, Vol.32 (5), p.2737-2764 [Periódico revisado por pares]

Philadelphia: Society for Industrial and Applied Mathematics

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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Raissi, M. ; Perdikaris, P. ; Karniadakis, G.E.

Journal of computational physics, 2019-02, Vol.378, p.686-707 [Periódico revisado por pares]

Cambridge: Elsevier Inc

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8
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
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Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

Beck, Christian ; E, Weinan ; Jentzen, Arnulf

Journal of nonlinear science, 2019-08, Vol.29 (4), p.1563-1619 [Periódico revisado por pares]

New York: Springer US

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9
Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
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Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

Alber, Mark ; Buganza Tepole, Adrian ; Cannon, William R ; De, Suvranu ; Dura-Bernal, Salvador ; Garikipati, Krishna ; Karniadakis, George ; Lytton, William W ; Perdikaris, Paris ; Petzold, Linda ; Kuhl, Ellen

NPJ digital medicine, 2019-11, Vol.2 (1), p.115-115, Article 115 [Periódico revisado por pares]

England: Nature Publishing Group

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Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease)
Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease)
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Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease)

Liang, Xing ; Zhang, Lei ; Zhao, Xiao-Qiang

Journal of dynamics and differential equations, 2019-09, Vol.31 (3), p.1247-1278 [Periódico revisado por pares]

New York: Springer US

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