Motivation: Because they effectively represent mass action kinetics, ordinary differential equation models are widely used to describe biochemical processes. Optimization-based calibration of these models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a prerequisite for many subsequent analysis steps, including uncertainty analysis, model selection and biological interpretation. Although multiple hypothesis have been advanced to explain why optimization based calibration of biochemical models is challenging, there are few comprehensive studies that test these hypothesis and tools for performing such studies are also lacking. Results: We implemented an established trust-region method as a modular python framework (fides) to enable structured comparison of different approaches to ODE model calibration involving Hessian approximation schemes and trust-region subproblem solvers. We evaluate fides on a set of benchmark problems that include experimental data. We find a high variability in optimizer performance among different implementations of the same algorithm, with fides performing more reliably that other implementations investigated. Our investigation of possible sources of poor optimizer performance identify shortcomings in the widely used Gauss-Newton approximation. We address these shortcomings by proposing a novel hybrid Hessian approximation scheme that enhances optimizer performance.
Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions
