DeepAI AI Chat
Log In Sign Up

Deep Runge-Kutta schemes for BSDEs

We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear parabolic partial differential equations. Our approach notably extends the one introduced in [Hure Pham Warin 2020] for the implicit Euler scheme to schemes which are more efficient in terms of discrete-time error. We establish some convergence results for our implemented schemes under classical regularity assumptions. We also illustrate the efficiency of our method for different schemes of order one, two and three. Our numerical results indicate that the Crank-Nicolson schemes is a good compromise in terms of precision, computational cost and numerical implementation.


page 1

page 2

page 3

page 4


Novel multi-step predictor-corrector schemes for backward stochastic differential equations

Novel multi-step predictor-corrector numerical schemes have been derived...

High-Order Multiderivative IMEX Schemes

Recently, a 4th-order asymptotic preserving multiderivative implicit-exp...

Curved Schemes for SDEs on Manifolds

Given a stochastic differential equation (SDE) in ℝ^n whose solution is ...

Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning

In this paper we enhance the well-known fifth order WENO shock-capturing...

An Analysis of the Milstein Scheme for SPDEs without a Commutative Noise Condition

In order to approximate solutions of stochastic partial differential equ...

Linearized Implicit Methods Based on a Single-Layer Neural Network: Application to Keller-Segel Models

This paper is concerned with numerical approximation of some two-dimensi...

An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware

Recently a splitting approach has been presented for the simulation of s...