Estimating and Assessing Differential Equation Models with Time-Course Data

TL;DR

This paper evaluates the MAGI method for estimating parameters and system trajectories of ODE models from noisy, incomplete time-course data, offering a computationally efficient alternative to traditional numerical integration.

Contribution

It demonstrates the effectiveness of MAGI in inferring ODE parameters and trajectories, including unobserved components, and in model assessment without numerical integration.

Findings

MAGI accurately infers parameters and trajectories from noisy data.

MAGI can assess and compare different ODE models efficiently.

MAGI bypasses the need for numerical integration in ODE analysis.

Abstract

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI's efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.