ODE Parameter Estimation Using Orthogonal Collocation

Tim15 min read·Just now

A Python Framework with Examples

If you wish to directly jump to the coding, scroll to the case study section below. First, I will go through some general introduction and some maths. 🤓

In my past, I have often been confronted with the challenge of finding parameters in a differential equation system. In my case, this usually happend when there was the need to describe a chemical reaction, or a growth of some cells over time. Estimating parameters for such “dynamical” systems is a foundational task in many disciplines, not only in chemistry and biology. For a system of ordinary differential equations (ODEs), often, the most straightforward approach is chosen to estimate parameters:

It all starts by setting up your ODE model of course. Sometimes, this approach is described by the “sequential approach”. For small systems or systems where we don’t have much noise, this is totally valid and works well. However, I encountered many cases where this methodoloy was unstable, inefficient, or sometimes did not end in a solution that was helpful, even after a long computational time.

Without going into the details of what solvers we can use inside this sequential approach or why things might go wrong, I would like to go over another topic in this tutorial. We explore an alternative…

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