Year: 2025
Type: preprint
Abstract: Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.
Source: arXiv (Cornell University)
Authors: Anderson, William, Chung, Seung Whan, Choi, Youngsoo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414969283
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