mlsanityData to 14 Oct 2026

Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems

arXiv 2609.37944 ↗First posted 29 Sep 2026stat.ML cs.LG math.DScited by 0

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Abstract (arXiv)

A wide range of methods have been proposed, including physics-informed neural networks, which are powerful but do not guarantee identifiability of the dynamics, symbolic regression, which requires a set of precomputed operations, and causal discovery, which is more principled but usually relies on strong assumptions that physical systems may violate. In this work, we develop a theory-grounded method and prove that under a set of permissive assumptions, the structural drivers and drift of stochastic delayed differential equations are identifiable. Our method outperforms others on a benchmark for driver identifiability, and on a second benchmark to evaluate physical consistency of the learned dynamics.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 30 of its 75 references that are in the map. First posted on arXiv 29 Sep 2026.

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30 of 75 references.

References · 30

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2017Improved Training of Wasserstein GANscited by 2,235
  3. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  4. 2017Learning Sparse Neural Networks through L0 Regularizationcited by 583
  5. 2019Augmented Neural ODEscited by 397
  6. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  7. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 200
  8. 2020AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularitycited by 144
  9. 2020Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasetscited by 137
  10. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 133
  11. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 98
  12. 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 95
18 more
  1. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  2. 2021Gradients are Not All You Needcited by 86
  3. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 64
  4. 2019Approximation Capabilities of Neural ODEs and Invertible Residual Networkscited by 56
  5. 2022Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learningcited by 44
  6. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  7. 2019Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRIcited by 41
  8. 2023CUTS+: High-dimensional Causal Discovery from Irregular Time-seriescited by 41
  9. 2019ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systemscited by 17
  10. 2023Enhancing Causal Discovery from Robot Sensor Data in Dynamic Scenarioscited by 17
  11. 2024When are dynamical systems learned from time series data statistically accurate?cited by 15
  12. 2022Sparsity in Continuous-Depth Neural Networkscited by 10
  13. 2025CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal modelscited by 8
  14. 2025Causal Climate Emulation with Bayesian Filteringcited by 5
  15. 2024Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systemscited by 4
  16. 2023Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimatescited by 2
  17. 2025Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equationscited by 2
  18. 2025Causal Structure Learning for Dynamical Systems with Theoretical Score Analysiscited by 2

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