Deep hybrid modeling of a HEK293 process: Combining long short-term memory networks with first principles equations

The combination of physical equations with deep learning is becoming a promising methodology for bioprocess digitalization. In this paper, we investigate for the first time the combination of long short-term memory (LSTM) networks with first principles equations in a hybrid workflow to describe human embryonic kidney 293 (HEK293) culture dynamics. Experimental data of 27 extracellular state variables in 20 fed-batch HEK293 cultures were collected in a parallel high throughput 250 mL cultivation system in an industrial process development setting. The adaptive moment estimation method with stochastic regularization and cross-validation were employed for deep learning. A total of 784 hybrid models with varying deep neural network architectures, depths, layers sizes and node activation functions were compared. In most scenarios, hybrid LSTM models outperformed classical hybrid Feedforward Neural Network (FFNN) models in terms of training and testing error. Hybrid LSTM models revealed to be less sensitive to data resampling than FFNN hybrid models. As disadvantages, Hybrid LSTM models are in general more complex (higher number of parameters) and have a higher computation cost than FFNN hybrid models. The hybrid model with the highest prediction accuracy consisted in a LSTM network with seven internal states connected in series with dynamic material balance equations. This hybrid model correctly predicted the dynamics of the 27 state variables (R² = 0.93 in the test data set), including biomass, key substrates, amino acids and metabolic by-products for around 10 cultivation days.