  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.
