用能量模型定义隐状态初始分布，实现连续时间序列建模与长时预测。
Latent Space Energy-based Neural ODEs
- 以能量模型构建隐状态先验，通过神经ODE驱动隐变量演化
- 在振荡系统、视频和真实运动数据上均优于现有方法
- 适合需要长期预测的动态系统建模任务
本文提出一种新型深度动力学模型，用于建模连续时间序列。该方法通过神经发射模型，将隐状态向量非线性变换生成时间序列中的每个数据点。隐状态的演化由神经微分方程（Neural ODE）隐式定义，其初始状态从由能量模型（EBM）参数化的信息性先验分布中采样。该框架进一步可解耦动态状态与潜在的静态变因，后者以隐空间中的时不变变量表示。模型采用最大似然估计结合马尔可夫链蒙特卡洛（MCMC）进行端到端训练。在振荡系统、视频及真实世界状态序列（MuJoCo）上的实验表明，采用可学习的能量先验的模型显著优于现有方法，并能泛化至新的动态参数化，支持长时程预测。
原文摘要 · Abstract (English)
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.
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