Beyond Predictions in Neural ODEs: Identification and Interventions

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.