Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the generalization properties of NODEs for dynamical systems beyond the observed data are underexplored. We systematically study the influence of weight and feature sparsity on forecasting as well as on identifying the underlying dynamical laws. Besides assessing existing methods, we propose a regularization technique to sparsify "input-output connections" and extract relevant features during training. Moreover, we curate real-world datasets consisting of human motion capture and human hematopoiesis single-cell RNA-seq data to realistically analyze different levels of out-of-distribution (OOD) generalization in forecasting and dynamics identification respectively. Our extensive empirical evaluation on these challenging benchmarks suggests that weight sparsity improves generalization in the presence of noise or irregular sampling. However, it does not prevent learning spurious feature dependencies in the inferred dynamics, rendering them impractical for predictions under interventions, or for inferring the true underlying dynamics. Instead, feature sparsity can indeed help with recovering sparse ground-truth dynamics compared to unregularized NODEs.

翻译：在准确恢复观察到的轨迹方面,在学习动态系统方面,普通神经差异(NODE)已证明是成功的。虽然为了提高稳健性,提出了不同种类的宽度建议,但除了观测到的数据之外,动态系统的内分泌系统一般化特性没有得到充分探讨。我们系统地研究重量和特征的宽度对预报的影响以及确定基本动态法的影响。除了评估现有方法外,我们建议采用一种正规化技术,在培训期间对“投入-产出连接”进行分解并提取相关特征。此外,我们整理由人类运动捕捉和人类肝脏单细胞RNA等值数据组成的真实世界数据集,以现实地分析预测和动态识别的不同程度。我们对这些具有挑战性的基准的广泛经验评估表明,重量的宽度提高了噪音或不规则抽样的普及程度。然而,它并不妨碍在推断动态中学习虚假特征,使得在干预下预测时不切实际的内置数据不切用,或将单细胞型RNA-等值数据用于实际分析分布和动态识别的不同水平。相反,我们对这些具有挑战性的基准性的基准性特征可以帮助恢复。