Deep Learning Schemes For Parabolic Nonlocal Integro-Differential Equations

2021/03/27 by Javier Castro, Castro, Javier · 3 citations
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Geotechnical and Geomechanical Engineering #Image Processing and 3D Reconstruction #Numerical Analysis (math.NA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2103.15008

openalex publication_date 2021/03/27 · openalex created_date 2022/10/28 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the numerical approximation of nonlocal integro differential parabolic equations via neural networks. These equations appear in many recent applications, including finance, biology and others, and have been recently studied in great generality starting from the work of Caffarelli and Silvestre. Based in the work by Hure, Pham and Warin, we generalize their Euler scheme and consistency result for Backward Forward Stochastic Differential Equations to the nonlocal case. We rely on Lèvy processes and a new neural network approximation of the nonlocal part to overcome the lack of a suitable good approximation of the nonlocal part of the solution.

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