# Marrying Causal Representation Learning with Dynamical Systems for Science

arXiv: https://arxiv.org/abs/2405.13888 · HTML: https://mlsanity.com/paper/2405.13888/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 74 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 30 of 44)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Identifiable Deep Generative Models via Sparse Decoding](https://mlsanity.com/paper/2110.10804/) (2021)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning](https://mlsanity.com/paper/2211.14666/) (2022)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [A Survey of Deep Learning for Scientific Discovery](https://mlsanity.com/paper/2003.11755/) (2020)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)

## Built on by (most cited first, 23 of 23)

- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Prediction-Powered Causal Inferences](https://mlsanity.com/paper/2502.06343/) (2025)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning](https://mlsanity.com/paper/2410.06074/) (2024)
- [Sanity Checking Causal Representation Learning on a Simple Real-World System](https://mlsanity.com/paper/2502.20099/) (2025)
- [Mechanistic PDE Networks for Discovery of Governing Equations](https://mlsanity.com/paper/2502.18377/) (2025)
- [The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representations](https://mlsanity.com/paper/2505.17708/) (2025)
- [Physically Interpretable World Models via Weakly Supervised Representation Learning](https://mlsanity.com/paper/2412.12870/) (2024)
- [Revealing Multimodal Causality with Large Language Models](https://mlsanity.com/paper/2509.17784/) (2025)
- [Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention](https://mlsanity.com/paper/2603.14483/) (2026)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- ["Cause" is Mechanistic Narrative within Scientific Domains: An Ordinary Language Philosophical Critique of "Causal Machine Learning"](https://mlsanity.com/paper/2501.05844/) (2025)
- [Towards Causal Representation Learning with Observable Sources as Auxiliaries](https://mlsanity.com/paper/2509.19058/) (2025)
- [Learning Explicit Single-Cell Dynamics Using ODE Representations](https://mlsanity.com/paper/2510.02903/) (2025)
- [ROPES: Robotic Pose Estimation via Score-Based Causal Representation Learning](https://mlsanity.com/paper/2510.20884/) (2025)
- [Diverse Dictionary Learning](https://mlsanity.com/paper/2604.17568/) (2026)
- [No Epoch Like the Present: Robust Climate Emulation Requires Out-of-Distribution Generalisation](https://mlsanity.com/paper/2605.22248/) (2026)
- [Learning Individual Dynamics from Sparse Cross-Sectional Snapshots](https://mlsanity.com/paper/2605.23470/) (2026)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)
- [Identifying ODEs from Unstructured Data with Causal Representation Learning](https://mlsanity.com/paper/2609.37083/) (2026)
- [Identifiable World Models from Pretrained Diffusion Representations](https://mlsanity.com/paper/2610.07028/) (2026)

## Abstract (arXiv)

Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any successful real-world application. At the same time, the field of dynamical systems benefited from deep learning and scaled to countless applications but does not allow parameter identification. In this paper, we draw a clear connection between the two and their key assumptions, allowing us to apply identifiable methods developed in causal representation learning to dynamical systems. At the same time, we can leverage scalable differentiable solvers developed for differential equations to build models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream tasks such as out-of-distribution classification or treatment effect estimation. We experiment with a wind simulator with partially known factors of variation. We also apply the resulting model to real-world climate data and successfully answer downstream causal questions in line with existing literature on climate change.