mlsanityData to 7 Oct 2026

Neural graphical modelling in continuous-time: consistency guarantees and algorithms

arXiv 2105.02522 ↗First posted 6 May 2021stat.ML cs.LG math.DScited by 42

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Abstract (arXiv)

The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define dependencies in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider score-based structure learning for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, least squares optimization with adaptive regularization schemes consistently recovers directed graphs of local independencies in systems of stochastic differential equations. Using this insight, we propose a score-based learning algorithm based on penalized Neural Ordinary Differential Equations (modelling the mean process) that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to outperform the state of the art across a range of dynamical systems.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). Builds on 20 of its 85 references that are in the map. First posted on arXiv 6 May 2021.

Builds on

20 of 85 references.

References · 20

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  3. 2019Causality for Machine Learningcited by 242
  4. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  5. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  6. 2019Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causalitycited by 55
  7. 2018Learning unknown ODE models with Gaussian processescited by 54
  8. 2021Interpretable Models for Granger Causality Using Self-explaining Neural Networkscited by 44
  9. 2014From Ordinary Differential Equations to Structural Causal Models: the deterministic casecited by 41
  10. 2016From Deterministic ODEs to Dynamic Structural Causal Modelscited by 32
  11. 2020Consistent Feature Selection for Analytic Deep Neural Networkscited by 27
  12. 2018Neural Granger Causalitycited by 19
8 more
  1. 2018On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variablescited by 19
  2. 2021Policy Analysis using Synthetic Controls in Continuous-Timecited by 18
  3. 2019ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systemscited by 17
  4. 2013Oracle Inequalities for High Dimensional Vector Autoregressionscited by 11
  5. 2016Network Reconstruction From High Dimensional Ordinary Differential Equationscited by 11
  6. 2020Learning Dynamic and Personalized Comorbidity Networks from Event Data using Deep Diffusion Processescited by 7
  7. 2018LASSO-Driven Inference in Time and Spacecited by 4
  8. 2016Inverse Problems for Matrix Exponential in System Identification: System Aliasingcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 4; 2023: 13; 2024: 8; 2025: 8; 2026: 7.

42 papers.

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  1. 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
  2. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  3. 2023CUTS+: High-dimensional Causal Discovery from Irregular Time-seriescited by 39
  4. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 35
  5. 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 32
  6. 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
  7. 2023Causal Modeling with Stationary Diffusionscited by 19
  8. 2023Hierarchical Graph Neural Networks for Causal Discovery and Root Cause Localizationcited by 18
  9. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  10. 2023Neural Structure Learning with Stochastic Differential Equationscited by 14
  11. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  12. 2024Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputationcited by 11
30 more
  1. 2022Sparsity in Continuous-Depth Neural Networkscited by 10
  2. 2024Jacobian Regularizer-based Neural Granger Causalitycited by 9
  3. 2022Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observationscited by 8
  4. 2023Generator Identification for Linear SDEs with Additive and Multiplicative Noisecited by 7
  5. 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equationscited by 7
  6. 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
  7. 2025CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal modelscited by 5
  8. 2025Inferring stochastic dynamics with growth from cross-sectional datacited by 4
  9. 2022Towards Better Long-range Time Series Forecasting using Generative Forecastingcited by 3
  10. 2026Foundation Inference Models for Ordinary Differential Equationscited by 3
  11. 2021Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Datacited by 2
  12. 2023CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Predictioncited by 2
  13. 2024Root-KGD: A Novel Framework for Root Cause Diagnosis Based on Knowledge Graph and Industrial Datacited by 2
  14. 2024LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Datacited by 2
  15. 2024CausalStock: Deep End-to-end Causal Discovery for News-driven Stock Movement Predictioncited by 2
  16. 2025Causal Structure Learning for Dynamical Systems with Theoretical Score Analysiscited by 2
  17. 2026Coarse-to-Fine Learning of Dynamic Causal Structurescited by 2
  18. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  19. 2021Towards Better Long-range Time Series Forecasting using Generative Adversarial Networkscited by 0
  20. 2023GDBN: a Graph Neural Network Approach to Dynamic Bayesian Networkcited by 0
  21. 2023Disentangled Causal Graph Learning for Online Unsupervised Root Cause Analysiscited by 0
  22. 2024ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulationscited by 0
  23. 2025SpinSVAR: Estimating Structural Vector Autoregression Assuming Sparse Inputcited by 0
  24. 2025Simulation-free Structure Learning for Stochastic Population Dynamicscited by 0
  25. 2025KarmaTS: A Universal Simulation Platform for Multivariate Time Series with Functional Causal Dynamicscited by 0
  26. 2026Integrating Causal DAGs in Deep RL: Activating Minimal Markovian States with Multi-Order Exposurecited by 0
  27. 2026Mask2Cause: Temporal Causal Discovery Beyond Causality in Meancited by 0
  28. 2026Causal Discovery on Irregular Time Seriescited by 0
  29. 2026ITSY: Causal Discovery From Irregular Time-Series Datacited by 0
  30. 2026Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systemscited by 0