# Beyond Predictions in Neural ODEs: Identification and Interventions

arXiv: https://arxiv.org/abs/2106.12430 · HTML: https://mlsanity.com/paper/2106.12430/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 56 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data](https://mlsanity.com/paper/1908.03190/) (2019)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [Neural Delay Differential Equations](https://mlsanity.com/paper/2102.10801/) (2021)
- [Stochasticity in Neural ODEs: An Empirical Study](https://mlsanity.com/paper/2002.09779/) (2020)
- [Learning stable and predictive structures in kinetic systems: Benefits of a causal approach](https://mlsanity.com/paper/1810.11776/) (2018)
- [Variable-lag Granger Causality for Time Series Analysis](https://mlsanity.com/paper/1912.10829/) (2019)

## Built on by (most cited first, 15 of 15)

- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints](https://mlsanity.com/paper/2306.09739/) (2023)
- [Sparsity in Continuous-Depth Neural Networks](https://mlsanity.com/paper/2210.14672/) (2022)
- [Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs](https://mlsanity.com/paper/2205.12550/) (2022)
- [Identifiability Challenges in Sparse Linear Ordinary Differential Equations](https://mlsanity.com/paper/2506.09816/) (2025)
- [AI for Science: An Emerging Agenda](https://mlsanity.com/paper/2303.04217/) (2023)
- [Identifiability Analysis of Linear ODE Systems with Hidden Confounders](https://mlsanity.com/paper/2410.21917/) (2024)
- [Causal Ordering for Structure Learning from Time Series](https://mlsanity.com/paper/2510.24639/) (2025)
- [NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2208.12771/) (2022)
- [Pruning neural network models for gene regulatory dynamics using data and domain knowledge](https://mlsanity.com/paper/2403.04805/) (2024)
- [Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations](https://mlsanity.com/paper/2512.13913/) (2025)
- [Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism](https://mlsanity.com/paper/2609.34566/) (2026)

## 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.