# Network Reconstruction From High Dimensional Ordinary Differential Equations

arXiv: https://arxiv.org/abs/1610.03177 · HTML: https://mlsanity.com/paper/1610.03177/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2016.

## Built on by (most cited first, 11 of 11)

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- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022)
- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [Calibrating multi-dimensional complex ODE from noisy data via deep neural networks](https://mlsanity.com/paper/2106.03591/) (2021)
- [Post-Regularization Confidence Bands for Ordinary Differential Equations](https://mlsanity.com/paper/2110.12510/) (2021)
- [Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems](https://mlsanity.com/paper/2507.20072/) (2025)
- [A scalable gene network model of regulatory dynamics in single cells](https://mlsanity.com/paper/2503.20027/) (2025)
- [Robust Learning of Heterogeneous Dynamic Systems](https://mlsanity.com/paper/2604.05285/) (2026)
- [Reconstruction of Enhanced Causal Omnidirectional Network (RECON)](https://mlsanity.com/paper/2607.21833/) (2026)

## Abstract (arXiv)

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system non-parametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches.