Learning Large Scale Ordinary Differential Equation Systems

TL;DR

This paper introduces the AIM algorithm and a framework for learning large-scale nonlinear ODE systems from data, effectively handling multiple environments and sparse network structures.

Contribution

The paper presents a novel adaptive integral matching (AIM) algorithm for efficiently learning polynomial and rational ODE systems with sparse networks from complex data.

Findings

AIM achieves state-of-the-art network recovery with an AUROC of 0.74 on DREAM challenge data.

AIM demonstrates good statistical properties and computational feasibility for large systems.

The framework accommodates data from multiple environments and interventions.

Abstract

Learning large scale nonlinear ordinary differential equation (ODE) systems from data is known to be computationally and statistically challenging. We present a framework together with the adaptive integral matching (AIM) algorithm for learning polynomial or rational ODE systems with a sparse network structure. The framework allows for time course data sampled from multiple environments representing e.g. different interventions or perturbations of the system. The algorithm AIM combines an initial penalised integral matching step with an adapted least squares step based on solving the ODE numerically. The R package episode implements AIM together with several other algorithms and is available from CRAN. It is shown that AIM achieves state-of-the-art network recovery for the in silico phosphoprotein abundance data from the eighth DREAM challenge with an AUROC of 0.74, and it is demonstrated via a range of numerical examples that AIM has good statistical properties while being computationally feasible even for large systems.