Training stiff neural ordinary differential equations with implicit single-step methods
Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of neural ODEs. In this paper, we propose an approach based on single-step implicit schemes to enable neural ODEs to handle stiffness and demonstrate that our implicit neural ODE method can learn stiff dynamics. This work addresses a key limitation in current neural ODE methods, paving the way for their use in a wider range of scientific problems.
Authors
- Linda Petzold (ORCID: https://orcid.org/0000-0001-6251-6078)
- Colby Fronk (ORCID: https://orcid.org/0000-0002-5943-1257)
Institutions
- University of California, Santa Barbara (US)
Publication Details
- Journal
- Chaos An Interdisciplinary Journal of Nonlinear Science
- Published
- 2024-12-01
- DOI
- https://doi.org/10.1063/5.0243382
- Citations
- 6
- Primary Topic
- Model Reduction and Neural Networks
- Type
- article
- Field-Weighted Citation Impact
- 1.69
Funders
- National Science Foundation
- China Scholarship Council
- University of California, Santa Barbara
- University of California, San Diego
- Materials Research Science and Engineering Center, Harvard University
- Office of the President, University of California
- National Institute of Biomedical Imaging and Bioengineering
- Division of Materials Research
- California NanoSystems Institute