Related papers: Deep splitting method for parabolic PDEs

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…

We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…

The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tackle functional nonlinearities involving gradient terms of any…

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…

Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations(PDE) by Beck et al. (SISC, V.43, 2021), named Deep Splitting method since they trained the Neural Networks step by step in the time direction. In…

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…

We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…