Regression using hybrid modelling approache#
Context#
In this notebook, we will consider a first principle Monod Kenetic model for cell growth.
The balances are described as follows for the biomass: $\( \dfrac{dX}{dt} = \mu * X \\ \)\( And the substrate: \)\( \dfrac{dS}{dt} = -\dfrac{1}{Y_{xs}} * \mu * X \)$
We will use this model to “generate” a dataset. We will assume the trye kenetics are unknown.
Objective:#
The idea here is to generate a few samples of intiail conditions and the above model. then we will assume that the exact kenetics are unknown then develop a model to predict \(\mu\) solely from the susbtrate concetration. the workflow is very similar to the previous tutorial only changes are:
Data generation is done two times: one to generate mu values for different \(X_0\) and \(S_0\)
Develop an ML model for predicting \(\mu\) from the substrate concetration
Integrate the ML model in a hybrid model where the \(\mu\) is generated by the ML model, while the ODE is solved mechanistically.
ML model of \(\mu\)#
To generate the data we first need to implement the model.