通过分阶段训练提升潜空间动态识别的精度与效率
Sequential decoder training for improved latent space dynamics identification
- 分阶段添加解码器，逐步修正前序阶段的残差误差
- 在1D-1V Vlasov方程上预测误差更低，训练时间更短
- 适合需要高精度物理模拟的科学计算场景
偏微分方程的精确数值求解在众多科学领域至关重要，但通常需要计算成本高昂的求解器，因此催生了降阶模型（ROM）。潜空间动态识别（LaSDI）是一种数据驱动的ROM框架，结合自编码器与方程发现，以学习可解释的潜空间动态。然而，在训练中强制潜空间动态会损害模型对仿真数据的重构精度。本文提出多阶段LaSDI（mLaSDI），通过顺序训练额外解码器来修正前期阶段的残差误差，从而提升重构与预测精度。在1D-1V Vlasov方程上的实验表明，mLaSDI在多种架构下均优于标准LaSDI，实现更低的预测误差和更短的训练时间。
原文摘要 · Abstract (English)
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.
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