Hybrid modeling, meaning the integration of data-driven and knowledge-based methods, is quickly gaining popularity among many research fields, including bioprocess engineering and development. Recently, the data-driven part of hybrid methods have been largely extended with machine learning algorithms (e.g., artificial neural network, support vector regression), while the mechanistic part is typically using differential equations to describe the dynamics of the process based on its current state. In this work we present an alternative hybrid model formulation that merges the advantages of Gaussian Process State Space Models and the numerical approximation of differential equation systems through full discretization. The use of Gaussian Process Models to describe complex bioprocesses in batch, fed-batch, has been reported in several applications. Nevertheless, handling the dynamics of the states of the system, known to have a continuous time-dependent evolution governed by implicit dynamics, has proven to be a major challenge. Discretization of the process on the sampling steps is a source of several complications, as are: 1) not being able to handle multi-rate date sets, 2) the step-size of the derivative approximation is defined by the sampling frequency, and 3) a high sensitivity to sampling and addition errors. We present a coupling of polynomial regression with Gaussian Process Models as representation of the right-hand side of the ordinary differential equation system and demonstrate the advantages in a typical fed-batch cultivation for monoclonal antibody production.
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
