Fetching the paper…
Reading the bibliography…
The recently introduced full-history recursive multilevel Picard (MLP) approximation methods have turned out to be quite successful in the numerical approximation of solutions of high-dimensional nonlinear PDEs.
Solving inverse problems in nonlinear PDEs by recurrent neural networks
1993
Earlier work this paper cites.
The numerical solution of linear ordinary differential equations by feedforward neural networks
1994
Earlier work this paper cites.
Diffusions, Markov processes and martingales. Vol. 2
1994
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
1998
Earlier work this paper cites.
Numerical solution of elliptic partial differential equation using radial basis function neural networks
2003
Earlier work this paper cites.
Probability theory
2006
Earlier work this paper cites.
2014
Earlier work this paper cites.
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
2015
Earlier work this paper cites.
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
2016
Earlier work this paper cites.
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
2017
Earlier work this paper cites.
Deep reinforcement learning for partial differential equation control
2017
Earlier work this paper cites.
Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs
2017
Earlier work this paper cites.
Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM
2017
Earlier work this paper cites.
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
2018
Earlier work this paper cites.
A unified deep artificial neural network approach to partial differential equations in complex geometries
2018
Earlier work this paper cites.
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
2018
Earlier work this paper cites.
DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing
2018
Earlier work this paper cites.
Solving high-dimensional partial differential equations using deep learning
2018
Earlier work this paper cites.
Convergence of the Deep BSDE Method for Coupled FBSDEs
2018
Earlier work this paper cites.
2018
Cited alongside, same era.
2018
Cited alongside, same era.
PDE-Net: Learning PDEs from Data
2018
Cited alongside, same era.
Neural networks trained to solve differential equations learn general representations
2018
Cited alongside, same era.
2018
Cited alongside, same era.
Space-time error estimates for deep neural network approximations for differential equations
2019
Later among the works it cites.
Deep neural network approximations for Monte Carlo algorithms
2019
Later among the works it cites.
2019
Later among the works it cites.
Some machine learning schemes for high-dimensional nonlinear PDEs
2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
DGM: A deep learning algorithm for solving partial differential equations
2018
Cited alongside, same era.
Deep splitting method for parabolic PDEs
2019
Cited alongside, same era.
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
2019
Cited alongside, same era.
On existence and uniqueness properties for solutions of stochastic fixed point equations
2019
Cited alongside, same era.
2019
Cited alongside, same era.
Deep optimal stopping
2019
Cited alongside, same era.
Solving high-dimensional optimal stopping problems using deep learning
2019
Cited alongside, same era.
2019
Later among the works it cites.
Deep PPDEs for rough local stochastic volatility
2019
Later among the works it cites.
A theoretical analysis of deep neural networks and parametric PDEs
2019
Later among the works it cites.
Deep learning observables in computational fluid dynamics
2019
Later among the works it cites.
Neural networks-based backward scheme for fully nonlinear PDEs
2019
Later among the works it cites.
2019
Later among the works it cites.
2020
Closest in time.
2020
Closest in time.
2020
Closest in time.
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
2020
Closest in time.
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients
2020
Closest in time.
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
2020
Closest in time.
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
2020
Closest in time.
Multilevel Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
2020
Closest in time.