Beyond Predictions in Neural ODEs: Identification and Interventions
Not on the map. Why?
Abstract (arXiv)
Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the rules that govern its evolution? Solving this task holds the great promise of fully understanding the causal interactions and being able to make reliable predictions about the system's behavior under interventions. We take a step towards answering this question for time-series data generated from systems of ordinary differential equations (ODEs). While the governing ODEs might not be identifiable from data alone, we show that combining simple regularization schemes with flexible neural ODEs can robustly recover the dynamics and causal structures from time-series data. Our results on a variety of (non)-linear first and second order systems as well as real data validate our method. We conclude by showing that we can also make accurate predictions under interventions on variables or the system itself.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 23 of its 56 references that are in the map. First posted on arXiv 23 Jun 2021.
Builds on
23 of 56 references.
References · 23
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
- 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
- 2019Augmented Neural ODEscited by 396
- 2018Neural Relational Inference for Interacting Systemscited by 339
- 2020Scalable Gradients for Stochastic Differential Equationscited by 264
- 2017Detecting causal associations in large nonlinear time series datasetscited by 240
- 2019Gradient-Based Neural DAG Learningcited by 227
- 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
- 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
- 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 182
11 more
- 2018Invariance, Causality and Robustnesscited by 123
- 2017Causal Structure Learningcited by 84
- 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
- 2020Bayesian Neural Ordinary Differential Equationscited by 44
- 2019NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Datacited by 42
- 2014From Ordinary Differential Equations to Structural Causal Models: the deterministic casecited by 41
- 2016From Deterministic ODEs to Dynamic Structural Causal Modelscited by 32
- 2021Neural Delay Differential Equationscited by 26
- 2020Stochasticity in Neural ODEs: An Empirical Studycited by 13
- 2018Learning stable and predictive structures in kinetic systems: Benefits of a causal approachcited by 12
- 2019Variable-lag Granger Causality for Time Series Analysiscited by 10
Built on by
Citing papers per year: 2022: 3; 2023: 5; 2024: 3; 2025: 3; 2026: 1.
15 papers.
Sort:
By area:
- 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
- 2023Simulation-free Schr"odinger bridges via score and flow matchingcited by 81
- 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
- 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
- 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
- 2022Sparsity in Continuous-Depth Neural Networkscited by 10
- 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
- 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equationscited by 7
- 2023AI for Science: An Emerging Agendacited by 5
- 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
- 2022NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systemscited by 1
- 2024Pruning neural network models for gene regulatory dynamics using data and domain knowledgecited by 1
- 2026Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism28 Sep 2026
- 2025Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations15 Dec 2025
- 2025Causal Ordering for Structure Learning from Time Series28 Oct 2025
- 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equations11 Jun 2025
- 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounders29 Oct 2024
- 2024Pruning neural network models for gene regulatory dynamics using data and domain knowledge5 Mar 2024
- 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes28 Feb 2024
- 2023Simulation-free Schr"odinger bridges via score and flow matching7 Jul 2023
- 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints16 Jun 2023
- 2023AI for Science: An Emerging Agenda7 Mar 2023
- 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets8 Feb 2023
- 2023Improving and generalizing flow-based generative models with minibatch optimal transport1 Feb 2023
3 more
- 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
- 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
- 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
- 2022Sparsity in Continuous-Depth Neural Networkscited by 10
- 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
- 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equationscited by 7
- 2023AI for Science: An Emerging Agendacited by 5
- 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
- 2022NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systemscited by 1
- 2024Pruning neural network models for gene regulatory dynamics using data and domain knowledgecited by 1
- 2025Causal Ordering for Structure Learning from Time Seriescited by 1
- 2025Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equationscited by 0
12 most cited of 13 All 13 (JSON)
- 2026Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism28 Sep 2026
- 2025Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations15 Dec 2025
- 2025Causal Ordering for Structure Learning from Time Series28 Oct 2025
- 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equations11 Jun 2025
- 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounders29 Oct 2024
- 2024Pruning neural network models for gene regulatory dynamics using data and domain knowledge5 Mar 2024
- 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes28 Feb 2024
- 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints16 Jun 2023
- 2023AI for Science: An Emerging Agenda7 Mar 2023
- 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets8 Feb 2023
- 2022Sparsity in Continuous-Depth Neural Networks26 Oct 2022
- 2022NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems26 Aug 2022
12 newest of 13 All 13 (JSON)