Author ORCID Identifier

https://orcid.org/0009-0009-3576-7977

Semester

Summer

Date of Graduation

2026

Document Type

Dissertation

Degree Type

PhD

Required Additional Files
ETD_Code.7z (2398 kB)
Code

College

Statler College of Engineering and Mineral Resources

Department

Mechanical and Aerospace Engineering

Committee Chair

Cosmin Dumitrescu

Committee Member

Hailin Li

Committee Member

Derek Johnson

Committee Member

Vyacheslav Akkerman

Committee Member

Jianli Hu

Abstract

The development of internal combustion engines for increased efficiency and reduced emissions demands improved design tools that are cost-effective, fast, and easy to integrate into existing engineering workflows. Low-dimensional physically based engine models serve this role by reducing the need for iterative experimental prototyping but historically rely on empirical correlations that sacrifice fidelity compared to CFD. Machine learning (ML) approaches, conversely, achieve high predictive accuracy but lack interpretability and generalize poorly beyond their training data. Physics-informed machine learning (PIML) bridges this gap by constraining the solution space to physically feasible predictions, offering a more reliable way to model in-cylinder phenomena. Chemical kinetics is a prime target for PIML. Its stiff differential equations dominate simulation run-time, so improving its computation can substantially increase both execution speed and the predictive capability for emissions such as NOx.

The current work presents a set of numerical models spanning physically-based and prediction-oriented ML approaches, all predicting NOx emissions from a heavy-duty diesel engine with varying degrees of speed and accuracy. The main contribution is a novel methodology and numerical tool that can be incorporated into emissions-focused engine modeling workflows for improved engine-out predictions. To the author's knowledge, this is also the first work to test and validate a NOx-predicting PINN autoregressively, i.e., with the model's own predictions successively fed back as inputs during simulation.

The developed models comprise a physically based one-dimensional (1D) engine model, a direct feed-forward neural network (direct NN), and three physics-informed neural network (PINN) models. The 1D model simulates all engine processes and computes NOx through its emissions sub-model. The direct NN predicts NOx from engine operating parameters in steady-state or transient conditions. The PINN models predict instantaneous in-cylinder NOx concentrations during combustion from conditions at intake-valve closing, each employing a different physical constraint or prediction method: atomic conservation of chemical species, thermal activation, and NOx formation rate. All models were validated against experimental data from a heavy-duty diesel engine (Navistar, Model 2021 E39 HD) tested as part of a broader research undertaking.

The 1D model predicted NOx with mean absolute errors of 11% in steady-state and 35% in transient operation. The direct NN achieved mean absolute percentage error of 5% for steady-state and a cumulative error of 0.03% transient operation, respectively. While all PINN models achieved relative validation errors below 10% in validation, autoregressive testing revealed markedly different levels of robustness among them, with the NOx-formation-rate-based PINN performing best in simulated practical deployment, with a relative error of 7.4%, and a 6.5% MAPE for NO prediction over 26 different engine cycles in rollout. These results demonstrate a clear advantage of combining physically based and ML approaches over either alone. The hybrid approach improves both the speed and accuracy of emissions prediction while grounding the overall engine model in consistent physics.

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