Related papers: Deep splitting method for parabolic PDEs

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…

In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In…

This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…

Semilinear parabolic partial differential equations (PDEs) are fundamental to modeling complex dynamical systems across scientific domains. The Deep Backward Stochastic Differential Equation (BSDE) method is a promising approach for…

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown…

An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…

Using probabilistic methods, we establish a-priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity which has quadratic growth in the…

How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for linear parabolic PDEs. We prove that our new method can be…

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…

Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…