StPINNs - Deep learning framework for approximation of stochastic differential equations

TL;DR

This paper introduces SPINNs, a neural network framework designed to approximate solutions of stochastic differential equations driven by Levy noise, providing a systematic mathematical approach.

Contribution

The paper presents a novel systematic framework for using neural networks to solve SDEs with Levy noise, advancing the field of stochastic modeling.

Findings

Framework effectively approximates solutions of SDEs with Levy noise

Provides a systematic mathematical foundation for neural network-based SDE solutions

Enhances the applicability of deep learning in stochastic differential equations

Abstract

In this paper, we introduce the SPINNs (stochastic physics-informed neural networks) in a systematic manner. This provides a mathematical framework for approximating the solution of stochastic differential equations (SDEs) driven by Levy noise using artificial neural networks.