Scalable nonlinear manifold reduced order model for dynamical systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916501364146176 |
|---|---|
| author | Zanardi, Ivan Diaz, Alejandro N. Chung, Seung Whan Panesi, Marco Choi, Youngsoo |
| author_facet | Zanardi, Ivan Diaz, Alejandro N. Chung, Seung Whan Panesi, Marco Choi, Youngsoo |
| contents | The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear subspace methods, NM-ROMs offer superior expressivity and enhanced reconstruction capabilities, while DD enables cost-effective, parallel training of autoencoders by partitioning the domain into algebraic subdomains. In this work, we investigate the scalability of this approach by implementing a "bottom-up" strategy: training NM-ROMs on smaller domains and subsequently deploying them on larger, composable ones. The application of this method to the two-dimensional time-dependent Burgers' equation shows that extrapolating from smaller to larger domains is both stable and effective. This approach achieves an accuracy of 1% in relative error and provides a remarkable speedup of nearly 700 times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable nonlinear manifold reduced order model for dynamical systems Zanardi, Ivan Diaz, Alejandro N. Chung, Seung Whan Panesi, Marco Choi, Youngsoo Numerical Analysis Dynamical Systems Computational Physics The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear subspace methods, NM-ROMs offer superior expressivity and enhanced reconstruction capabilities, while DD enables cost-effective, parallel training of autoencoders by partitioning the domain into algebraic subdomains. In this work, we investigate the scalability of this approach by implementing a "bottom-up" strategy: training NM-ROMs on smaller domains and subsequently deploying them on larger, composable ones. The application of this method to the two-dimensional time-dependent Burgers' equation shows that extrapolating from smaller to larger domains is both stable and effective. This approach achieves an accuracy of 1% in relative error and provides a remarkable speedup of nearly 700 times. |
| title | Scalable nonlinear manifold reduced order model for dynamical systems |
| topic | Numerical Analysis Dynamical Systems Computational Physics |
| url | https://arxiv.org/abs/2412.00507 |