Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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

Liu, Donglin LU and Sopasakis, Alexandros LU orcid (2025) 14th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems, DYCOPS 2025 In IFAC-PapersOnLine 59(6). p.379-384
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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Artificial intelligence and machine learning, Dynamic modelling and simulation for control and operation, Modeling and identification
in
IFAC-PapersOnLine
volume
59
issue
6
pages
6 pages
publisher
IFAC Secretariat
conference name
14th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems, DYCOPS 2025
conference location
Bratislava, Slovakia
conference dates
2025-06-16 - 2025-06-19
external identifiers
  • scopus:105013961452
ISSN
2405-8971
DOI
10.1016/j.ifacol.2025.07.175
language
English
LU publication?
yes
additional info
Publisher Copyright: Copyright © 2025 The Authors.
id
4bc19769-0e9c-4ff3-9a6f-4d3452bc948c
date added to LUP
2025-09-04 05:48:35
date last changed
2025-10-14 12:54:50
@article{4bc19769-0e9c-4ff3-9a6f-4d3452bc948c,
  abstract     = {{<p>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.</p>}},
  author       = {{Liu, Donglin and Sopasakis, Alexandros}},
  issn         = {{2405-8971}},
  keywords     = {{Artificial intelligence and machine learning; Dynamic modelling and simulation for control and operation; Modeling and identification}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{6}},
  pages        = {{379--384}},
  publisher    = {{IFAC Secretariat}},
  series       = {{IFAC-PapersOnLine}},
  title        = {{A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise}},
  url          = {{http://dx.doi.org/10.1016/j.ifacol.2025.07.175}},
  doi          = {{10.1016/j.ifacol.2025.07.175}},
  volume       = {{59}},
  year         = {{2025}},
}