Scalable nonlinear manifold reduced order model for dynamical systems

Autor:	Zanardi, Ivan, Diaz, Alejandro N., Chung, Seung Whan, Panesi, Marco, Choi, Youngsoo
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Mathematics - Dynamical Systems Physics - Computational Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: To be included in the proceedings of the Machine Learning and the Physical Sciences Workshop at NeurIPS 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.00507 Zobrazit plný text záznamu View this record from Arxiv