Modeling: Mechanistic or Statistical ? Part 2 : Making a choice
Interested by knowing the differences between statistical and mechanistic approach?
All modeling approaches need to be fed with experimental data to identify parameters. A fair question to ask is which approach is more demanding in terms of experimental information.
Not sure that there is a definitive answer, but trends can be given. An important consideration is the number of variables that should be investigated, and the number of parameters associated with each model. Clearly, the higher the number of parameters, the higher the number of experiments required.
Because Statistical models are not based on physical understanding, they often require larger number of parameters and thus large amounts of data to correlate trends and patterns. In essence, increasing number of parameters reflects the move from linear to quadratic or even higher order models. Coming back to the satellite example, using three experimental positions to fit a quadratic expression instead of a straight line, would certainly not really improve the prediction ability.
Philosophically, if a “clever” mechanistic model requires more parameters than a “clueless” statistical model for doing the same thing, there is a problem! The art of modeling is to identify and to focus on the description of key underlying phenomena: the real issue is not the number of parameters, but to which extend key underlying phenomena have been captured. Assume one wants to model a bioreactor; refining highly sophisticated metabolic scheme maybe useless if the system is limited by poor mixing or oxygen flux.
As usual, a fair way to address the problematic of making a choice is to define objectives:
- If you simply want to fit a few experimental results, statistical models are clearly an option
- If you want to predict “inside the box”, both approaches can be considered
- If you want to predict what occurs “outside the box” (scaling-up, changing compositions, operating protocols …) only the mechanistic approach can be considered.
Then another important consideration is to check what is available in terms of knowledge, time and resources.
Regarding the mechanistic approach, do you have at least a skeleton of a model (for instance you know stoichiometries and the only thing left is to determine kinetics) ? If that is the case, a few well-chosen experiments may allow you to complete your mechanistic model.
If you don’t have ideas on how to build a mechanistic model, according to the situations, this may take you from one day to several lives... Building mechanistic models is a science and an art.
The below table is a summary of our philosophy related to model selection.
Finally, there is no rule forbidding to associate the two approaches in the so-called hybrid models. This sophisticated approach may be promising by proposing the best of the two worlds. Insufficient preparation and understanding may however lead to get the worse and not the best of the two worlds? We will discuss this in a subsequent blog.
The case of Chromatography
Chromatography is a very interesting subject for mechanistic modeling: it is a time/space dependent nonlinear system, involving partial differential equations sand algebraic equation that can be associated with extreme stiffness and thus numerical difficulties.
Ypso-Facto has a strong expertise and a long list of successful projects in industrial chromatography. These successes allowed us to progressively build our own understanding of the physico-chemical phenomena taking place in numerous chromatography process all over the world.
Our software Ypso-Ionic embeds this large knowledge to propose the most advanced mechanistic models for chromatography systems in a user-friendly interface.
At Ypso-Facto, we can help you develop mechanistic models which can then be used in Ypso-Ionic, an innovative software tool for designing chromatographic processes! Challenge us!
Interest readers may have a look at:
Author : Roger-Marc Nicoud
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