Modern applications increasingly require unsupervised learning of latent dynamics from high-dimensional time-series. This presents a significant challenge of identifiability: many abstract latent representations may reconstruct observations, yet do they guarantee an adequate identification of the governing dynamics? This paper investigates this challenge from two angles: the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification. We combine these two strategies in a novel framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD) with: 1) a latent dynamic function that hybridize known mathematical expressions of prior physics with neural functions describing its unknown errors, and 2) a meta-learning formulation to learn to separately identify both components of the hybrid dynamics. Through extensive experiments on five physics and one biomedical systems, we provide strong evidence for the benefits of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to observed data.

翻译：现代应用日益需要从高维时间序列中无监督学习潜动态。这带来了一个显著的识别挑战：许多抽象的潜在表示可能重建观测，但能否保证对控制动态的充分识别？本文从两个角度研究这一挑战：针对所建模数据的物理归纳偏倚使用，以及一种将预测目标与用于识别的数据分离的学习识别策略。我们将这两种策略结合在一个新颖的无监督混合潜动态元学习框架（Meta-HyLaD）中，该框架包含：1）一个潜动态函数，将先验物理的已知数学表达式与描述其未知误差的神经函数混合；2）一个元学习公式，用于学习分别识别混合动态的两个组成部分。通过在五个物理系统和一个生物医学系统上的大量实验，我们为Meta-HyLaD在整合丰富先验知识的同时识别其与观测数据差距的益处提供了有力证据。