# Inferring networks from time series: a neural approach

arXiv: https://arxiv.org/abs/2303.18059 · HTML: https://mlsanity.com/paper/2303.18059/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 71 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm](https://mlsanity.com/paper/2012.12810/) (2020)
- [Neural parameter calibration for large-scale multi-agent models](https://mlsanity.com/paper/2209.13565/) (2022)
- [Stochastic Modelling of Urban Structure](https://mlsanity.com/paper/1805.03567/) (2018)

## Built on by (most cited first, 7 of 7)

- [Identifiable learning of dissipative dynamics](https://mlsanity.com/paper/2510.24160/) (2025)
- [Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel](https://mlsanity.com/paper/2402.08412/) (2024)
- [Neural parameter calibration and uncertainty quantification for epidemic forecasting](https://mlsanity.com/paper/2312.03147/) (2023)
- [Modelling Global Trade with Optimal Transport](https://mlsanity.com/paper/2409.06554/) (2024)
- [SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations](https://mlsanity.com/paper/2503.05993/) (2025)
- [Learning Multi-type heterogeneous interacting particle systems](https://mlsanity.com/paper/2602.03954/) (2026)
- [Deep learning four decades of human migration](https://mlsanity.com/paper/2506.22821/) (2025)

## Abstract (arXiv)

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of the dynamics to which they give rise. In this work we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of non-linear dynamics, which we demonstrate by learning an entire cost matrix for a non-linear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.