Computationally Efficient LSTM–Euler Hybrid Model Framework: Application to Industrial-Scale Fermentation with Experimental Validation

Industrial-scale fermentation processes are subject to significant variability due to fluctuating raw material quality, seed culture performance, and environmental disturbances, which challenge the assumptions of static-parameter first-principles models. This study introduces a hybrid modeling framework that integrates a first-principles fermentation model with a long short-term memory (LSTM) neural network to dynamically estimate kinetic parameters in real time. The LSTM receives a five-time-step rolling window of virtual or experimental measurements comprising biomass, substrates, product, dissolved oxygen, and feed flow rates and outputs time-varying estimates of kinetic parameters, such as growth rates, yield coefficients, and inhibition constants. These parameters are then input into the first-principles model, which evolves the system states using Euler’s method. Comparative analysis against two baseline models (i.e., a physics-integrated feedforward neural network and an LSTM–ODEint model) demonstrated superior predictive accuracy and computational tractability for the developed model. Temporal error and runtime analyses confirmed that the proposed LSTM–Euler architecture achieves faster convergence, smoother training, and lower loss in comparison to traditional neural network (NN)-based hybrid models. The LSTM component captures batch-to-batch variations that conventional hybrid models miss, while the fixed-step Euler solver avoids the instability introduced by adaptive solvers, leading to stable gradient flows and consistent parameter updates. This combination enables higher predictive accuracy with reduced computational overhead, offering performance gains over existing hybrid modeling implementations.