提升潜空间动力学模型长期预测精度，解决物理模拟中误差累积问题。
Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics
- 采用高阶低开销有限差分法建模潜空间动态
- 引入滚动损失函数，实现任意时间跨度的精准预测
- 适用于需要长时间模拟的物理系统建模任务
求解复杂的偏微分方程在物理科学中至关重要，但通常依赖计算成本高昂的数值方法。降维模型（ROMs）通过维度压缩实现快速近似。尽管现代ROMs能处理参数化的偏微分方程族，其预测性能随时间推移显著下降。本文提出两种改进：(1) 设计一种灵活、高阶且计算开销低的有限差分方案；(2) 提出滚动损失（Rollout loss），训练ROM在任意时间跨度上保持高精度。我们在二维伯格斯方程（2D Burgers equation）上验证了该方法的有效性。
原文摘要 · Abstract (English)
Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast approximations. While modern ROMs can solve parameterized families of PDEs, their predictive power degrades over long time horizons. We address this by (1) introducing a flexible, high-order, yet inexpensive finite-difference scheme and (2) proposing a Rollout loss that trains ROMs to make accurate predictions over arbitrary time horizons. We demonstrate our approach on the 2D Burgers equation.
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