Work

A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise

Year: 2025

Type: article

Abstract: We propose data-driven surrogate models to solve systems of time-dependent differential equations coupled with noise. Using a feedforward neural network, we separately learn the noise and solution, tackling approximations across regimes with bifurcations and rare events. Focusing on irregular data generated by a stochastic noise model on a one-dimensional spatial lattice coupled to a differential equation, we examine two profiles: the periodic complex Ginzburg-Landau equation and a saddle bifurcation equation exhibiting rare events. This coupling introduces conditional data, enabling solutions to reach new states while posing challenges for accurately learning the underlying dynamics.

Source: IFAC-PapersOnLine

DOI: 10.1016/j.ifacol.2025.07.175

Authors: Donglin Liu, Alexandros Sopasakis

Institution: Lund University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Svenska Forskningsrådet Formas, Vetenskapsrådet

Awards: G2485834667, NAISS