mlsanityData to 7 Oct 2026

Discovering Causal Relations and Equations from Data

arXiv 2305.13341 ↗First posted 21 May 2023physics.data-an cs.AI cs.LGcited by 33

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Abstract (arXiv)

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 92 of its 439 references that are in the map. First posted on arXiv 21 May 2023.

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92 of 439 references.

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38 more
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Citing papers per year: 2023: 5; 2024: 10; 2025: 14; 2026: 4.

33 papers.

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  1. 2024Large Language Models for Constrained-Based Causal Discoverycited by 15
  2. 2023Do AI models produce better weather forecasts than physics-based models? A quantitative evaluation case study of Storm Ciar'ancited by 12
  3. 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inferencecited by 12
  4. 2023Equilibrium in the Computing Continuum through Active Inferencecited by 9
  5. 2024Causal Graph Neural Networks for Wildfire Danger Predictioncited by 7
  6. 2025Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discoverycited by 7
  7. 2025AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledgecited by 5
  8. 2026Explainable AI: Learning from the Learnerscited by 4
  9. 2024Response Theory via Generative Score Modelingcited by 3
  10. 2024Decoding complexity: how machine learning is redefining scientific discoverycited by 3
  11. 2024AI for Extreme Event Modeling and Understanding: Methodologies and Challengescited by 3
  12. 2024Earth System Data Cubes: Avenues for advancing Earth system researchcited by 3
21 more
  1. 2023On the choice of training data for machine learning of geostrophic mesoscale turbulencecited by 2
  2. 2025An analysis of optimization problems involving ReLU neural networkscited by 2
  3. 2025Deep Koopman operator framework for causal discovery in nonlinear dynamical systemscited by 2
  4. 2025Discovering equations from data: symbolic regression in dynamical systemscited by 2
  5. 2025Analyzing Generalization in Pre-Trained Symbolic Regressioncited by 2
  6. 2025Electron neural closure for turbulent magnetosheath simulations: energy channelscited by 2
  7. 2023Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learningcited by 1
  8. 2024Machine-learning invariant foliations in forced systems for reduced order modellingcited by 1
  9. 2025Quantum-enhanced causal discovery for a small number of samplescited by 1
  10. 2025Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networkscited by 1
  11. 2025Beyond Accuracy and Complexity: The Effective Information Criterion for Structurally Stable Symbolic Regressioncited by 1
  12. 2026Physics-Informed Neural Networks for Biological 2D+t Reaction-Diffusion Systemscited by 1
  13. 2023Projecting infinite time series graphs to finite marginal graphs using number theorycited by 0
  14. 2024Causal machine learning for sustainable agroecosystemscited by 0
  15. 2024Discovery and inversion of the viscoelastic wave equation in inhomogeneous mediacited by 0
  16. 2025MXMap: A Multivariate Cross Mapping Framework for Causal Discovery in Dynamical Systemscited by 0
  17. 2025Scientific machine learning in Hydrology: a unified perspectivecited by 0
  18. 2025Leveraging Teleconnections with Physics-Informed Graph Attention Networks for Long-Range Extreme Rainfall Forecasting in Thailandcited by 0
  19. 2025The Machine Learning Approach to Moment Closure Relations for Plasma: A Reviewcited by 0
  20. 2026Learning Causal Structure of Time Series using Best Order Score Searchcited by 0
  21. 2026Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equationscited by 0