A hybrid modeling approach combining machine learning and physical phenomenological methods to predict highly transient engine emissions

Abstract Climate change has made low-emission propulsion technologies an increasingly important focus of development. Battery-electric vehicles (BEVs), which operate locally emission-free and offer high overall efficiency, are one possible solution. However, they are limited by charging infrastructure and comparatively short ranges in the compact and midsize segments. Hybrid-electric vehicles (HEVs) can mitigate these disadvantages and can reduce fuel consumption and emissions relative to purely internal-combustion-engine vehicles. Full exploitation of these benefits requires dedicated operating strategies that can be developed efficiently in simulation environments—provided that precise models of the vehicle subsystems and the environment are available. This work investigates various approaches for modeling emissions during highly transient engine operation, with an emphasis on forecasting emissions under real-driving conditions. Purely physics-based models are computationally expensive and lose fidelity during transients, whereas purely data-driven models require large, carefully curated data sets. Accordingly, this paper proposes a novel single hybrid architecture that combines a physical-phenomenological combustion/emission model with a long short-term memory (LSTM) network through a lightweight gray-box fusion layer to predict NO $$_x$$ , CO, CO $$_2$$ , and THC. Machine-learning methods outperform the physical-phenomenological model in dynamic scenarios, achieving an RMSE of 0.0401 on the test cycle, computed on min–max normalized emission signals (scaled to the range [0, 1] based on the training data). The model is therefore suitable for real-time control and optimization tasks. The parallel hybrid model further improves this result by approximately 25%, demonstrating that a data-based model can be enhanced with physical information without increasing the training effort.