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Calibration of automotive engines to ensure compliance with emission regulations is a critical phase in product development. Control of engine-out particulate emissions, which directly impact the environment and public health, is particularly important. Detailed physics-based models are typically used to gain a rich understanding of the complex physical phenomena that drive the soot particle formation in an engine cylinder. However, such models often fail to correctly represent the highly dynamic nature of the underlying mechanisms under transient combustion conditions. Moreover, most physics-based models were initially developed for diesel engine applications and their applicability to gasoline engines remains questionable due to differences in flame structure and fuel-wall interactions. Black-box models have been previously proposed to predict engine-out soot emissions, but their lack of physical interpretability is an unsolved drawback. To address these limitations, we present a physics-aware twin-model machine learning framework to predict and analyze engine-out soot mass from a gasoline direct injection (GDI) engine. The framework combines a physics-based model with a bagging-type ensemble learning model that both maintains high accuracy and allows physical interpretation of results without using computationally intensive high-fidelity models. This work shows why a one-model-fits-all approach fails in the case of predicting soot emissions due to clustered co-occurrences of operating conditions that cause non-compliant behavior. We compare the performance of the proposed framework with that of the standalone baseline model and a feed-forward deep neural network. Using WLTP data from a 2.0L naturally aspirated GDI engine, the proposed framework predicts engine-out soot mass with an improvement of 29% in the R² value and 21% in the root mean squared error from the baseline physics-based model, without compromising physical interpretability. These improvements are significant enough to warrant further framework development with additional engine datasets. 

The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are threefold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws governing vehicle dynamics into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods. *The full version of the paper can be accessed at https://arxiv.org/abs/2301.05739