A novel prior-informed machine learning model for diesel engine emission estimation

The increasing complexity of internal combustion engines, coupled with stringent emission regulations, has made virtualization essential for efficient and effective exploration of engine design spaces. This evolution demands predictive models that balance accuracy with computational efficiency, particularly when applied to emission estimation tasks. Data-driven approaches have been widely adopted in this field due to their flexibility and strong predictive capabilities. However, achieving high accuracy with these methods typically requires large training datasets. To overcome this limitation, this study explores the application of Gradient-Informed Neural Networks (GradINNs) for diesel-engine emission prediction. GradINN combines a primary neural network, responsible for the emission estimates, with an auxiliary network that encodes prior beliefs about the gradients of the output with respect to the model’s input parameters. A specialized loss function enforces consistency between the predicted gradients and these prior beliefs. The proposed model is benchmarked against traditional data-driven approaches, specifically Neural Networks (NNs) and Gaussian Process Regression (GPR), using data from both a Design of Experiments (DoE) campaign and an engine map. Results demonstrate that GradINN consistently outperforms both benchmark methods across key emission targets, including nitrogen oxides, particulate matter, unburned hydrocarbons, and carbon monoxide. The proposed approach achieves lower prediction errors and improved generalization, notably maintaining comparable accuracy with up to 25 % fewer training samples compared to the best-performing benchmark, highlighting its potential to reduce experimental effort without compromising accuracy.