How to check and improve optimization

The challenge

Parameter optimization of ODE models is challenging because

• there is no analytical solution of the ODEs, thus the objective function (and derivatives) can only be evaluated numerically with limited accuracy
• the objective function depends non-linearly on the parameters
• models might be large, i.e. have many parameters
• the amount of available data and observables is typically restricted which yields non-identifiability
• usually only rough knowledge is available about parameter ranges
• additional numerical challenges like events have to be accounted for

It is therefore essential to ensure that optimization works reliably.

Guidelines for reliable optimization

• Apply multistart-optimization (e.g. arFitLHS) in order to guarantee that
• the optimization algorithms converges (at least locally), i.e. an optimum is found repeatedly
• a found optimum is indeed (likeli) the global one

Checks for reliable optimization

Literature

Lessons Learned from Quantitative Dynamical Modeling in Systems Biology