Efficient inference for differential equation models without numerical solvers

TL;DR

This paper introduces a novel inference method for differential equation models that avoids numerical solvers, thereby eliminating truncation errors and improving the reliability of parameter estimation in biological data analysis.

Contribution

The authors propose a solver-free inference approach for differential equation models, reducing computational complexity and avoiding errors caused by numerical solutions.

Findings

Method successfully eliminates the need for numerical solvers.

Open-source Jupyter notebooks facilitate implementation.

Approach improves inference accuracy by removing truncation errors.

Abstract

Parameter inference is essential when interpreting observational data using mathematical models. Standard inference methods for differential equation models typically rely on obtaining repeated numerical solutions of the differential equation(s). Recent results have explored how numerical truncation error can have major, detrimental, and sometimes hidden impacts on likelihood-based inference by introducing false local maxima into the log-likelihood function. We present a straightforward approach for inference that eliminates the need for solving the underlying differential equations, thereby completely avoiding the impact of truncation error. Open-access Jupyter notebooks, available on GitHub, allow others to implement this method for a broad class of widely-used models to interpret biological data.