Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning (Q5019943)

scientific article; zbMATH DE number 7455604

Language	Label	Description	Also known as
English	Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning	scientific article; zbMATH DE number 7455604

Statements

instance of

scholarly article

0 references

title

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning (English)

0 references

zbMATH Open document ID

1490.60202

0 references

DOI

10.1088/1361-6544/ac337f

0 references

0 references

0 references

0 references

0 references

11 January 2022

0 references

full work available at URL

https://arxiv.org/abs/2008.13333

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

partial differential equations

0 references

high dimension

0 references

nonlinear Monte Carlo

0 references

deep learning

0 references

backward stochastic differential equations

0 references

Wikidata QID

Q114096634

0 references

describes a project that uses

0 references

0 references

0 references

0 references

0 references

MaRDI publication profile

0 references

0 references

0 references

Pricing and hedging derivative securities in markets with uncertain volatilities

0 references

A quantization algorithm for solving multidimensional discrete-time optimal stopping problems

0 references

Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

0 references

Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations

0 references

On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations

0 references

Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations

0 references

Deep optimal stopping

0 references

Solving high-dimensional optimal stopping problems using deep learning

0 references

Q3241581

0 references

A forward scheme for backward SDEs

0 references

A PRIMAL–DUAL ALGORITHM FOR BSDES

0 references

Deep learning as optimal control problems: models and numerical methods

0 references

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

0 references

Stochastic Methods for Solving High-Dimensional Partial Differential Equations

0 references

Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

0 references

Q5309942

0 references

Simulation of BSDEs by Wiener chaos expansion

0 references

Solving the quantum many-body problem with artificial neural networks

0 references

Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case

0 references

Structure-preserving deep learning

0 references

Machine learning for semi linear PDEs

0 references

A branching particle system approximation for a class of FBSDEs

0 references

COUNTERPARTY RISK AND FUNDING: THE FOUR WINGS OF THE TVA

0 references

Probabilistic methods for semilinear partial differential equations. Applications to finance

0 references

Solving Backward Stochastic Differential Equations Using the Cubature Method: Application to Nonlinear Pricing

0 references

Second order discretization of backward SDEs and simulation with the cubature method

0 references

On the Monte Carlo simulation of BSDEs: an improvement on the Malliavin weights

0 references

Algorithms for overcoming the curse of dimensionality for certain Hamilton-Jacobi equations arising in control theory and elsewhere

0 references

A forward-backward stochastic algorithm for quasi-linear PDEs

0 references

Recursive valuation of defaultable securities and the timing of resolution of uncertainty

0 references

A proposal on machine learning via dynamical systems

0 references

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

0 references

A mean-field optimal control formulation of deep learning

0 references

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

0 references

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

0 references

Machine learning from a continuous viewpoint. I

0 references

The Barron space and the flow-induced function spaces for neural network models

0 references

The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

0 references

DNN expression rate analysis of high-dimensional PDEs: application to option pricing

0 references

Q5189317

0 references

A probabilistic numerical method for fully nonlinear parabolic PDEs

0 references

Solving electrical impedance tomography with deep learning

0 references

Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs

0 references

Simulation of BSDEs with jumps by Wiener chaos expansion

0 references

Multilevel Monte Carlo Path Simulation

0 references

Multilevel Monte Carlo Methods

0 references

Solving BSDE with Adaptive Control Variate

0 references

A regression-based Monte Carlo method to solve backward stochastic differential equations

0 references

Stratified Regression Monte-Carlo Scheme for Semilinear PDEs and BSDEs with Large Scale Parallelization on GPUs

0 references

Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions

0 references

Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression

0 references

Uniform error estimates for artificial neural network approximations for heat equations

0 references

A monotone scheme for high-dimensional fully nonlinear PDEs

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Convergence of the deep BSDE method for coupled FBSDEs

0 references

Solving high-dimensional eigenvalue problems using deep neural networks: a diffusion Monte Carlo like approach

0 references

Solving many-electron Schrödinger equation using deep neural networks

0 references

Monte Carlo complexity of global solution of integral equations

0 references

Q4433869

0 references

Monte Carlo complexity of parametric integration

0 references

A numerical algorithm for a class of BSDEs via the branching process

0 references

Branching diffusion representation of semilinear PDEs and Monte Carlo approximation

0 references

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria

0 references

Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle

0 references

Deep backward schemes for high-dimensional nonlinear PDEs

0 references

Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities

0 references

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

0 references

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

0 references

Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

0 references

Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

0 references

An Approximate Dynamic Programming Algorithm for Monotone Value Functions

0 references

Algorithms of data generation for deep learning and feedback design: a survey

0 references

Solving for high-dimensional committor functions using artificial neural networks

0 references

SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems

0 references

A parallel algorithm for solving BSDEs

0 references

Mean field games. I: The stationary case

0 references

Mean field games. II: Finite horizon and optimal control

0 references

Mean field games

0 references

Neural algorithm for solving differential equations

0 references

Q4558489

0 references

Deep learning observables in computational fluid dynamics

0 references

Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov

0 references

Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations

0 references

Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space

0 references

Q4029028

0 references

Forward-backward stochastic differential equations and quasilinear parabolic PDEs

0 references

Feynman-Kac representation of fully nonlinear PDEs and applications

0 references

Neural networks-based backward scheme for fully nonlinear PDEs

0 references

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

0 references

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

0 references

Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

0 references

A Dual Method For Evaluation of Dynamic Risk in Diffusion Processes

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

Branching Diffusion Processes

0 references

Q4404383

0 references

Q4626283

0 references

Numerical solution of parabolic equations in high dimensions

0 references

Nesting Monte Carlo for high-dimensional non-linear PDEs

0 references

On the branching process for Brownian particles with an absorbing boundary

0 references

Weak adversarial networks for high-dimensional partial differential equations

0 references

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

0 references

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

0 references

A numerical scheme for BSDEs

0 references

DP-GEN: a concurrent learning platform for the generation of reliable deep learning based potential energy models

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:5019943