This paper introduces novel deep dynamical models designed to represent continuous-time sequences. Our approach employs a neural emission model to generate each data point in the time series through a non-linear transformation of a latent state vector. The evolution of these latent states is implicitly defined by a neural ordinary differential equation (ODE), with the initial state drawn from an informative prior distribution parameterized by an Energy-based model (EBM). This framework is extended to disentangle dynamic states from underlying static factors of variation, represented as time-invariant variables in the latent space. We train the model using maximum likelihood estimation with Markov chain Monte Carlo (MCMC) in an end-to-end manner. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts, and can generalize to new dynamic parameterization, enabling long-horizon predictions.

翻译：本文提出了一种新颖的深度动态模型，旨在表示连续时间序列。我们的方法采用神经发射模型，通过对隐状态向量进行非线性变换来生成时间序列中的每个数据点。这些隐状态的演化由神经常微分方程（ODE）隐式定义，其初始状态则从由能量模型（EBM）参数化的信息性先验分布中采样。该框架进一步扩展，以将动态状态与潜在的静态变异因子解耦，后者在隐空间中表示为时不变变量。我们采用马尔可夫链蒙特卡洛（MCMC）方法，通过端到端的最大似然估计来训练模型。在振荡系统、视频以及真实世界状态序列（MuJoCo）上的实验结果表明，我们具有可学习能量先验的模型优于现有同类模型，并且能够泛化到新的动态参数化设置，从而实现长时程预测。