PINN-Cast：探索连续深度NODE在Transformer中的作用及物理信息损失作为短期天气预报中的软物理约束
PINN-Cast: Exploring the Role of Continuous-Depth NODE in Transformers and Physics Informed Loss as Soft Physical Constraints in Short-term Weather Forecasting
AI总结：
本文提出连续深度Transformer编码器，结合Neural ODE动态和物理信息损失，提升短期天气预报的准确性与物理一致性。
摘要：
操作性天气预测长期以来依赖于基于物理的数值天气预测（NWP），其准确性以巨大的计算成本和复杂的模拟工作流程为代价。最近的基于Transformer的预报器提供了高效的基于数据的替代方案，但Transformer是物理无关的模型。此外，标准Transformer编码器通过离散层更新演变表示，可能不如建模平滑潜在动态适合。本文提出了一种连续深度的Transformer编码器，用于天气预测，其中每个编码器块内集成了神经普通微分方程（Neural ODE）动态。具体而言，我们用基于ODE的更新替代离散残差更新，通过自适应数值积分求解。我们还引入了双分支注意力模块，结合传统逐块自注意力与辅助分支，应用导数操作到注意力日志，提供额外的变化敏感交互信号。为进一步使预测与支配原理一致，我们提出了一种定制的物理信息训练目标，将物理一致性作为软约束。我们评估了所提出方法与标准离散Transformer基线和现有连续时间Neural ODE预测变体的对比，证明了PINN-Cast在短期天气预测中的重要性。
英文摘要：
Operational weather prediction has long relied on physics-based numerical weather prediction (NWP), whose accuracy comes at the cost of substantial compute and complex simulation workflows. Recent transformer-based forecasters offer efficient data-driven alternatives, however transformers are physics-agnostic models. Additionally, standard transformer encoders evolve representations through discrete layer updates that may be less suited to modeling smooth latent dynamics. In this work, we propose a continuous-depth transformer encoder for weather forecasting that integrates Neural Ordinary Differential Equation (Neural ODE) dynamics within each encoder block. Specifically, we replace discrete residual updates with ODE-based updates solved using adaptive numerical integration. We also introduce a two-branch attention module that combines conventional patch-wise self-attention with an auxiliary branch that applies a derivative operator to attention logits, providing an additional change-sensitive interaction signal. To further align forecasts with governing principles, we propose a customized physics-informed training objective that enforces physical consistency as a soft constraint. We evaluate the proposed method against a standard discrete transformer baseline and an existing continuous-time Neural ODE forecasting variant, demonstrating the importance of PINN-Cast in short term weather forecasting.
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