Neural Laplace for learning Stochastic Differential Equations

TL;DR

Neural Laplace provides a unified framework for learning various differential equations, including stochastic ones, outperforming traditional neural network methods for ODEs and extending applicability to SDEs.

Contribution

This work extends Neural Laplace to stochastic differential equations, offering both theoretical insights and practical methods for modeling SDEs with neural networks.

Findings

Outperforms existing neural network approaches for ODEs

Demonstrates potential for learning SDEs from data

Provides theoretical foundations for Neural Laplace in stochastic settings

Abstract

Neural Laplace is a unified framework for learning diverse classes of differential equations (DE). For different classes of DE, this framework outperforms other approaches relying on neural networks that aim to learn classes of ordinary differential equations (ODE). However, many systems can't be modelled using ODEs. Stochastic differential equations (SDE) are the mathematical tool of choice when modelling spatiotemporal DE dynamics under the influence of randomness. In this work, we review the potential applications of Neural Laplace to learn diverse classes of SDE, both from a theoretical and a practical point of view.