mlsanityData to 14 Oct 2026

From Ordinary Differential Equations to Structural Causal Models: the deterministic case

arXiv 1408.2063 ↗First posted 9 Aug 2014cs.AIcited by 41

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Abstract (arXiv)

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Aug 2014.

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Citing papers per year: 2021: 11; 2022: 7; 2023: 6; 2024: 6; 2025: 8; 2026: 3.

41 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  2. 2021Towards Causal Representation Learningcited by 209
  3. 2022Amortized Inference for Causal Structure Learningcited by 90
  4. 2022Diffusion Causal Models for Counterfactual Estimationcited by 87
  5. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  6. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  7. 2022From Statistical to Causal Learningcited by 40
  8. 2023Discovering Causal Relations and Equations from Datacited by 36
  9. 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
  10. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  11. 2023Causal Modeling with Stationary Diffusionscited by 19
  12. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
29 more
  1. 2021Dynamic Causal Bayesian Optimizationcited by 17
  2. 2021Causal Multi-Agent Reinforcement Learning: Review and Open Problemscited by 16
  3. 2021Beyond Predictions in Neural ODEs: Identification and Interventionscited by 15
  4. 2023Targeted Reduction of Causal Modelscited by 15
  5. 2022Sparsity in Continuous-Depth Neural Networkscited by 10
  6. 2022Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observationscited by 8
  7. 2025CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal modelscited by 8
  8. 2021Normalized multivariate time series causality analysis and causal graph reconstructioncited by 7
  9. 2022Phenomenological Causalitycited by 7
  10. 2023Generator Identification for Linear SDEs with Additive and Multiplicative Noisecited by 7
  11. 2025Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbationscited by 6
  12. 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
  13. 2021Causality and independence in perfectly adapted dynamical systemscited by 4
  14. 2024A Practical Approach to Causal Inference over Timecited by 4
  15. 2025Counterfactual reasoning: an analysis of in-context emergencecited by 4
  16. 2025Counterfactual Probabilistic Diffusion with Expert Modelscited by 4
  17. 2021Learning soft interventions in complex equilibrium systemscited by 2
  18. 2022A Causal Research Pipeline and Tutorial for Psychologists and Social Scientistscited by 2
  19. 2025Causal Structure Learning for Dynamical Systems with Theoretical Score Analysiscited by 2
  20. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  21. 2024Extending Structural Causal Models for Autonomous Vehicles to Simplify Temporal System Construction & Enable Dynamic Interactions Between Agentscited by 1
  22. 2025A New Perspective On AI Safety Through Control Theory Methodologiescited by 1
  23. 2025Towards Causal Representation Learning with Observable Sources as Auxiliariescited by 1
  24. 2021An overview of the quantitative causality analysis and causal graph reconstruction based on a rigorous formalism of information flowcited by 0
  25. 2024A Dynamical View of the Question of Whycited by 0
  26. 2024Identification and Estimation of the Bi-Directional MR with Some Invalid Instrumentscited by 0
  27. 2025Cyclic Counterfactuals under Shift-Scale Interventionscited by 0
  28. 2026Vector Space of Cyclescited by 0
  29. 2026Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equationscited by 0