Current deep learning models for dynamics forecasting struggle with generalization. They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder which infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on both turbulent flow and real-world ocean data forecasting tasks.

翻译：DyAd 有两个部分:一个编码器,它以薄弱的监管来推断任务中的时间变化隐藏特征,另一个预报器,它学习整个域的共享动态。编码器在使用适应性实例和适应性倾斜的推论期间调整和控制预报器。理论上,我们证明这种程序的一般错误与源域的任务关联性以及源和目标之间的域差异有关。我们实验性地证明,我们的模型在动荡流和真实世界海洋数据预测任务上都超越了最新的最新方法。