Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910427749810176 |
|---|---|
| author | Michałowska, Katarzyna Goswami, Somdatta Karniadakis, George Em Riemer-Sørensen, Signe |
| author_facet | Michałowska, Katarzyna Goswami, Somdatta Karniadakis, George Em Riemer-Sørensen, Signe |
| contents | Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data. Existing methods, however, cannot extrapolate accurately and are prone to error accumulation in long-time integration. Herein, we address this issue by combining neural operators with recurrent neural networks, learning the operator mapping, while offering a recurrent structure to capture temporal dependencies. The integrated framework is shown to stabilize the solution and reduce error accumulation for both interpolation and extrapolation of the Korteweg-de Vries equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks Michałowska, Katarzyna Goswami, Somdatta Karniadakis, George Em Riemer-Sørensen, Signe Machine Learning Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data. Existing methods, however, cannot extrapolate accurately and are prone to error accumulation in long-time integration. Herein, we address this issue by combining neural operators with recurrent neural networks, learning the operator mapping, while offering a recurrent structure to capture temporal dependencies. The integrated framework is shown to stabilize the solution and reduce error accumulation for both interpolation and extrapolation of the Korteweg-de Vries equation. |
| title | Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2303.02243 |