Three ways to solve partial differential equations with neural networks — A review
Published 2021 View Full Article
- Home
- Publications
- Publication Search
- Publication Details
Title
Three ways to solve partial differential equations with neural networks — A review
Authors
Keywords
-
Journal
GAMM Mitteilungen
Volume 44, Issue 2, Pages -
Publisher
Wiley
Online
2021-05-28
DOI
10.1002/gamm.202100006
References
Ask authors/readers for more resources
Related references
Note: Only part of the references are listed.- Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Numerical Applications
- (2021) Achref Bachouch et al. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
- Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
- (2021) Fabian Laakmann et al. ADVANCES IN COMPUTATIONAL MATHEMATICS
- Physics-Informed Deep Learning for Computational Elastodynamics without Labeled Data
- (2021) Chengping Rao et al. JOURNAL OF ENGINEERING MECHANICS
- Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
- (2020) Liu Yang et al. SIAM JOURNAL ON SCIENTIFIC COMPUTING
- Constraint-aware neural networks for Riemann problems
- (2020) Jim Magiera et al. JOURNAL OF COMPUTATIONAL PHYSICS
- The neural particle method – An updated Lagrangian physics informed neural network for computational fluid dynamics
- (2020) Henning Wessels et al. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
- Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
- (2020) Ameya D. Jagtap et al. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
- Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements
- (2020) XIAOLI CHEN et al. EUROPEAN JOURNAL OF APPLIED MATHEMATICS
- Deep learning observables in computational fluid dynamics
- (2020) Kjetil O. Lye et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
- (2020) Christian Beck et al. Journal of Numerical Mathematics
- Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
- (2020) Ameya D. Jagtap et al. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
- The concept of velocity in the history of Brownian motion
- (2020) Arthur Genthon European Physical Journal H
- On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
- (2020) Jérôme Darbon et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
- (2020) Martin Hutzenthaler et al. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
- Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
- (2019) Christian Beck et al. JOURNAL OF NONLINEAR SCIENCE
- On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations
- (2019) Weinan E et al. JOURNAL OF SCIENTIFIC COMPUTING
- Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
- (2019) Pierre Henry-Labordère et al. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
- Neural-net-induced Gaussian process regression for function approximation and PDE solution
- (2019) Guofei Pang et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- (2019) Yinhao Zhu et al. JOURNAL OF COMPUTATIONAL PHYSICS
- A deep learning solution approach for high-dimensional random differential equations
- (2019) Mohammad Amin Nabian et al. PROBABILISTIC ENGINEERING MECHANICS
- A deep energy method for finite deformation hyperelasticity
- (2019) Vien Minh Nguyen-Thanh et al. EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
- Deep ReLU networks and high-order finite element methods
- (2019) Joost A. A. Opschoor et al. Analysis and Applications
- Physics-informed neural networks for high-speed flows
- (2019) Zhiping Mao et al. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
- A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
- (2019) Xuhui Meng et al. JOURNAL OF COMPUTATIONAL PHYSICS
- A First-Order Numerical Scheme for Forward-Backward Stochastic Differential Equations in Bounded Domains
- (2018) Jie Yang et al. JOURNAL OF COMPUTATIONAL MATHEMATICS
- Hidden physics models: Machine learning of nonlinear partial differential equations
- (2018) Maziar Raissi et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- (2018) Maziar Raissi et al. SIAM JOURNAL ON SCIENTIFIC COMPUTING
- Optimization Methods for Large-Scale Machine Learning
- (2018) Léon Bottou et al. SIAM REVIEW
- DGM: A deep learning algorithm for solving partial differential equations
- (2018) Justin Sirignano et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Optimal approximation of piecewise smooth functions using deep ReLU neural networks
- (2018) Philipp Petersen et al. NEURAL NETWORKS
- A unified deep artificial neural network approach to partial differential equations in complex geometries
- (2018) Jens Berg et al. NEUROCOMPUTING
- Solving high-dimensional partial differential equations using deep learning
- (2018) Jiequn Han et al. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
- Increasing compound events of extreme hot and dry days during growing seasons of wheat and maize in China
- (2018) You Lu et al. Scientific Reports
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- (2018) M. Raissi et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Machine learning of linear differential equations using Gaussian processes
- (2017) Maziar Raissi et al. JOURNAL OF COMPUTATIONAL PHYSICS
- Convergence analysis of a finite element method for second order non-variational elliptic problems
- (2017) Michael Neilan Journal of Numerical Mathematics
- Error bounds for approximations with deep ReLU networks
- (2017) Dmitry Yarotsky NEURAL NETWORKS
- Julia: A Fresh Approach to Numerical Computing
- (2017) Jeff Bezanson et al. SIAM REVIEW
- Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations
- (2017) E. Gobet et al. STOCHASTIC PROCESSES AND THEIR APPLICATIONS
- Data-driven discovery of partial differential equations
- (2017) Samuel H. Rudy et al. Science Advances
- Deep vs. shallow networks: An approximation theory perspective
- (2016) H. N. Mhaskar et al. Analysis and Applications
- Numerical simulation of quadratic BSDEs
- (2016) Jean-François Chassagneux et al. ANNALS OF APPLIED PROBABILITY
- A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA
- (2016) Pierre Henry-Labordère et al. SIAM Journal on Financial Mathematics
- A PRIMAL-DUAL ALGORITHM FOR BSDES
- (2015) Christian Bender et al. MATHEMATICAL FINANCE
- Deep learning
- (2015) Yann LeCun et al. NATURE
- Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients
- (2014) Iain Smears et al. SIAM JOURNAL ON NUMERICAL ANALYSIS
- Linear Multistep Schemes for BSDEs
- (2014) Jean-François Chassagneux SIAM JOURNAL ON NUMERICAL ANALYSIS
- A numerical algorithm for a class of BSDEs via the branching process
- (2013) Pierre Henry-Labordère et al. STOCHASTIC PROCESSES AND THEIR APPLICATIONS
- Finite element approximations of the three dimensional Monge-Ampère equation
- (2012) Susanne Cecelia Brenner et al. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
- BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS-PART I: PRICING
- (2012) Stéphane Crépey MATHEMATICAL FINANCE
- Stochastic ordinary differential equations in applied and computational mathematics
- (2011) D. J. Higham IMA JOURNAL OF APPLIED MATHEMATICS
- Two Numerical Methods for the elliptic Monge-Ampère equation
- (2010) Jean-David Benamou et al. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
- What you should know about approximate dynamic programming
- (2009) Warren B. Powell NAVAL RESEARCH LOGISTICS
- Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
- (2009) Xiaobing Feng et al. SIAM JOURNAL ON NUMERICAL ANALYSIS
- Multilevel Monte Carlo Path Simulation
- (2008) Michael B. Giles OPERATIONS RESEARCH
Find Funding. Review Successful Grants.
Explore over 25,000 new funding opportunities and over 6,000,000 successful grants.
ExplorePublish scientific posters with Peeref
Peeref publishes scientific posters from all research disciplines. Our Diamond Open Access policy means free access to content and no publication fees for authors.
Learn More