Fides: Reliable Trust-Region Optimization for Parameter Estimation of Ordinary Differential Equation Models

Abstract

Ordinary differential equation (ODE) models are widely used to describe biochemical processes, since they effectively represent mass action kinetics. Optimization-based calibration of ODE models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a prerequisite for uncertainty analysis, model comparison, and biological interpretation. Multiple hypotheses have been advanced to explain why optimization based calibration of biochemical models is challenging, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking.

We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving various Hessian approximation schemes. We evaluated fides on a set of benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same algorithm. Overall, fides performed most reliably and efficiently. Our investigation of possible sources of poor optimizer performance identified drawbacks in the widely used Gauss-Newton, BFGS and SR1 Hessian approximations. We address these drawbacks by proposing a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. We expect fides to be broadly useful for ODE constrained optimization problems and to enable future methods development.