  Cultivation experiments often produce sparse and irregular time series.
Classical approaches based on mechanistic models, like Maximum Likelihood
fitting or Monte-Carlo Markov chain sampling, can easily account for sparsity
and time-grid irregularities, but most statistical and Machine Learning tools
are not designed for handling sparse data out-of-the-box. Among popular
approaches there are various schemes for filling missing values (imputation)
and interpolation into a regular grid (alignment). However, such methods
transfer the biases of the interpolation or imputation models to the target
model. We show that Deep Set Neural Networks equipped with triplet encoding of
the input data can successfully handle bio-process data without any need for
imputation or alignment procedures. The method is agnostic to the particular
nature of the time series and can be adapted for any task, for example, online
monitoring, predictive control, design of experiments, etc. In this work, we
focus on forecasting. We argue that such an approach is especially suitable for
typical cultivation processes, demonstrate the performance of the method on
several forecasting tasks using data generated from macrokinetic growth models
under realistic conditions, and compare the method to a conventional fitting
procedure and methods based on imputation and alignment.

Machine Learning