# Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines

arXiv: https://arxiv.org/abs/2304.13799 · HTML: https://mlsanity.com/paper/2304.13799/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 26 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [How important are activation functions in regression and classification? A survey, performance comparison, and future directions](https://mlsanity.com/paper/2209.02681/) (2022)
- [Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks](https://mlsanity.com/paper/2211.08761/) (2022)

## Built on by (most cited first, 6 of 6)

- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [MyCrunchGPT: A chatGPT assisted framework for scientific machine learning](https://mlsanity.com/paper/2306.15551/) (2023)
- [Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks](https://mlsanity.com/paper/2310.03001/) (2023)
- [A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoring](https://mlsanity.com/paper/2412.11967/) (2024)
- [Correctness Verification of Neural Networks Approximating Differential Equations](https://mlsanity.com/paper/2402.07621/) (2024)
- [Bayesian Calibration of Engine-out NOx Models for Engine-to-Engine Transferability](https://mlsanity.com/paper/2511.18178/) (2025)

## Abstract (arXiv)

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance requirements. The PINN model is applied to diesel engines with a variable-geometry turbocharger and exhaust gas recirculation, using measurement data of selected state variables. The results demonstrate the ability of the PINN model to predict simultaneously both unknown parameters and dynamics accurately with both clean and noisy data, and the importance of the self-adaptive weight in the loss function for faster convergence. The input data for these simulations are derived from actual engine running conditions, while the outputs are simulated data, making this a practical case study of PINN's ability to predict real-world dynamical systems. The mean value model of the diesel engine incorporates empirical formulae to represent certain states, but these formulae may not be generalizable to other engines. To address this, the study considers the use of deep neural networks (DNNs) in addition to the PINN model. The DNNs are trained using laboratory test data and are used to model the engine-specific empirical formulae in the mean value model, allowing for a more flexible and adaptive representation of the engine's states. In other words, the mean value model uses both the PINN model and the DNNs to represent the engine's states, with the PINN providing a physics-based understanding of the engine's overall dynamics and the DNNs offering a more engine-specific and adaptive representation of the empirical formulae. By combining these two approaches, the study aims to offer a comprehensive and versatile approach to monitoring the health and performance of diesel engines.