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arXiv · 2412.00507

Scalable nonlinear manifold reduced order model for dynamical systems

Ivan Zanardi·Alejandro N. Diaz·Seung Whan Chung·Marco Panesi·Youngsoo Choi
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Abstract

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.

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Ivan Zanardi, Alejandro N. Diaz, Seung Whan Chung, Marco Panesi, Youngsoo Choi. 2024-11-30. Scalable nonlinear manifold reduced order model for dynamical systems. https://arxiv.org/abs/2412.00507

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