Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these paradigms can improve identifiability, stability, and robustness. However, real dynamical systems often exhibit cyclic interactions and nonstationarity, whereas many causal discovery methods rely on acyclicity, stationarity, or equilibrium assumptions. We propose an integrative causal discovery framework for dynamical systems that leverages partial physical knowledge through stochastic differential equations (SDEs). The drift term encodes known ODE dynamics, while the diffusion term captures unknown causal couplings beyond the prescribed physics. We develop a scalable sparsity-inducing maximum quasi-likelihood estimator with a theoretically justified stabilization technique to improve the optimization landscape. Under mild conditions, we establish causal graph recovery guarantees for both stable and unstable SDEs. We also analyze robustness of our causal graph estimate to ODE misspecification and clarify how the introduced stabilization technique balances numerical stability and statistical recoverability. Experiments on linear SDEs and nonlinear benchmarks, including Lotka-Volterra and Lorenz dynamics with acyclic and cyclic structures, show improved graph recovery and robustness over data-driven baselines. We also demonstrate practical utility on real-world epidemic data by reconstructing stochastic SIR dynamics within our causal discovery framework.

翻译：因果发现是一种用于分析复杂系统的数据驱动范式，而基于物理的模型（如常微分方程）则为真实世界动态过程提供了机理结构。融合这些范式可提升可识别性、稳定性和鲁棒性。然而，实际动态系统常呈现循环交互和非平稳性，多数因果发现方法却依赖于无环性、平稳性或平衡态假设。本文提出一种面向动态系统的整合性因果发现框架，通过随机微分方程利用部分物理知识：漂移项编码已知的常微分方程动态，扩散项则捕获超出预设物理机制的未知因果耦合。我们设计了一种可扩展的稀疏诱导极大拟似然估计器，并采用理论上合理的稳定化技术优化优化景观。在温和条件下，我们建立了稳定与非稳定随机微分方程的因果图恢复保证准则。同时，分析了因果图估计对常微分方程误设的鲁棒性，阐明了所引入的稳定化技术如何在数值稳定性和统计可恢复性间取得平衡。在线性随机微分方程及非线性基准（含Lotka-Volterra和Lorenz动态的环状与无环结构）上的实验表明，相较于数据驱动基线，该方法在因果图恢复与鲁棒性方面均有提升。通过因果发现框架重构随机SIR动态，我们还在真实疫情数据中验证了其实用价值。