Beyond Predictions in Neural ODEs: Identification and Interventions

2021-06-23

arXiv.org

AI Summary

This work addresses the problem of jointly identifying dynamical laws and causal structure from observed time-series data generated by ordinary differential equation (ODE)-driven systems, while enabling counterfactual prediction under interventions. We propose a novel neural ODE framework that—uniquely—integrates lightweight sparsity and symmetry regularization to achieve robust dynamics modeling and causal graph learning even under non-identifiable conditions. The method unifies the representation of inter-variable dynamics and causal dependencies, supporting explicit intervention inference on both variables and system parameters. Evaluated across diverse synthetic benchmarks—including linear and nonlinear first- and second-order ODE systems—as well as real-world datasets, our approach significantly improves dynamical reconstruction accuracy and counterfactual prediction reliability, while enhancing causal interpretability through structured, sparse, and symmetric Jacobian estimation.

Abstract

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.

Problem

• Differential Equations
• Machine Learning
• Causal Inference

Innovation

• Differential Equations
• Neural Networks
• Causal Inference