用物理约束对齐时间序列，解决偏微分方程模型的误差累积问题。
Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models
- 通过自监督学习融合物理约束，对齐不同时间步的物理动态。
- 在长时序外分布数据上显著提升模型准确率与鲁棒性。
- 无需已知物理先验，适用于未知或复杂动力系统建模。
自回归偏微分方程（PDE）基础模型在处理时变数据方面展现出巨大潜力，但其自回归预测机制存在深层的捷径问题，导致误差积累。这一问题在分布外数据上尤为突出，下游任务中长期动态的表现可能接近随机初始化。为此，我们提出物理信息时间对齐（PITA），一种受反问题求解启发的自监督学习框架。PITA通过将物理信息约束融入自监督信号，在不依赖已知物理先验的前提下，对每条给定的PDE轨迹上不同时间步的物理动态进行对齐。实验表明，PITA能显著提升现有基础模型在多种时变PDE数据上的准确性与鲁棒性。代码已开源：https://github.com/SCAILab-USTC/PITA。
原文摘要 · Abstract (English)
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing error accumulation. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to the out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at https://github.com/SCAILab-USTC/PITA.
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