# Causal models for dynamical systems

arXiv: https://arxiv.org/abs/2001.06208 · HTML: https://mlsanity.com/paper/2001.06208/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 30 of 34)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference](https://mlsanity.com/paper/2403.10766/) (2024)
- [Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past](https://mlsanity.com/paper/2203.06056/) (2022)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Exploring Causal Learning through Graph Neural Networks: An In-depth Review](https://mlsanity.com/paper/2311.14994/) (2023)
- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [Learning by Doing: Controlling a Dynamical System using Causality, Control, and Reinforcement Learning](https://mlsanity.com/paper/2202.06052/) (2022)
- [ODE-based Recurrent Model-free Reinforcement Learning for POMDPs](https://mlsanity.com/paper/2309.14078/) (2023)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning](https://mlsanity.com/paper/2303.03181/) (2023)
- [Counterfactual reasoning: an analysis of in-context emergence](https://mlsanity.com/paper/2506.05188/) (2025)
- [Learning soft interventions in complex equilibrium systems](https://mlsanity.com/paper/2112.05729/) (2021)
- [Investigating Sindy As a Tool For Causal Discovery In Time Series Signals](https://mlsanity.com/paper/2212.14133/) (2022)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [Interpretable (not just posthoc-explainable) medical claims modeling for discharge placement to prevent avoidable all-cause readmissions or death](https://mlsanity.com/paper/2208.12814/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [Identifying Elasticities in Autocorrelated Time Series Using Causal Graphs](https://mlsanity.com/paper/2409.15530/) (2024)
- [Towards Identifiability of Interventional Stochastic Differential Equations](https://mlsanity.com/paper/2505.15987/) (2025)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2106.02600/) (2021)
- [A Dynamical View of the Question of Why](https://mlsanity.com/paper/2402.10240/) (2024)

## Abstract (arXiv)

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to model the behaviour under interventions. It can been taken as a starting point to answer a plethora of causal questions, including the identification of causal effects or causal structure learning. In this chapter, we provide a natural and straight-forward extension of this concept to dynamical systems, focusing on continuous time models. In particular, we introduce two types of causal kinetic models that differ in how the randomness enters into the model: it may either be considered as observational noise or as systematic driving noise. In both cases, we define interventions and therefore provide a possible starting point for causal inference. In this sense, the book chapter provides more questions than answers. The focus of the proposed causal kinetic models lies on the dynamics themselves rather than corresponding stationary distributions, for example. We believe that this is beneficial when the aim is to model the full time evolution of the system and data are measured at different time points. Under this focus, it is natural to consider interventions in the differential equations themselves.