Causal discovery is often a data-driven paradigm to analyze complex real-world systems. In parallel, physics-based models such as ordinary differential equations (ODEs) provide mechanistic structure for many dynamical processes. Integrating these paradigms potentially allows physical knowledge to act as an inductive bias, improving identifiability, stability, and robustness of causal discovery in dynamical systems. However, such integration remains challenging: real dynamical systems often exhibit feedback, cyclic interactions, and non-stationary data trend, while many widely used causal discovery methods are formulated under acyclicity or equilibrium-based assumptions. In this work, we propose an integrative causal discovery framework for dynamical systems that leverages partial physical knowledge as an inductive bias. Specifically, we model system evolution as a stochastic differential equation (SDE), where the drift term encodes known ODE dynamics and the diffusion term corresponds to unknown causal couplings beyond the prescribed physics. We develop a scalable sparsity-inducing MLE algorithm that exploits causal graph structure for efficient parameter estimation. Under mild conditions, we establish guarantees to recover the causal graph. Experiments on dynamical systems with diverse causal structures show that our approach improves causal graph recovery and produces more stable, physically consistent estimates than purely data-driven state-of-the-art baselines.

翻译：因果发现通常是一种数据驱动范式，用于分析复杂的现实世界系统。与此同时，基于物理的模型（如常微分方程）为许多动态过程提供了机制性结构。整合这两种范式有可能使物理知识作为一种归纳偏置，从而提高动态系统中因果发现的可识别性、稳定性和鲁棒性。然而，这种整合仍然具有挑战性：真实的动态系统通常表现出反馈、循环相互作用和非平稳数据趋势，而许多广泛使用的因果发现方法是在无环性或基于平衡的假设下构建的。在这项工作中，我们提出了一个用于动态系统的整合性因果发现框架，该框架利用部分物理知识作为归纳偏置。具体而言，我们将系统演化建模为一个随机微分方程，其中漂移项编码已知的常微分方程动力学，而扩散项对应于超出规定物理范围的未知因果耦合。我们开发了一种可扩展的稀疏性诱导最大似然估计算法，该算法利用因果图结构进行高效的参数估计。在温和条件下，我们建立了恢复因果图的保证。在具有不同因果结构的动态系统上的实验表明，与纯粹数据驱动的先进基线方法相比，我们的方法改善了因果图的恢复，并产生了更稳定、物理上更一致的估计。