A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoring

Improving diesel engine efficiency, reducing emissions, and enabling robust health monitoring have been critical research topics in engine modelling. While recent advancements in the use of neural networks for system monitoring have shown promising results, such methods often focus on component-level analysis, lack generalizability, and physical interpretability. In this study, we propose a novel hybrid framework that combines physics-informed neural networks (PINNs) with deep operator networks (DeepONet) to enable accurate and computationally efficient parameter identification in mean-value diesel engine models. Our method leverages physics-based system knowledge in combination with data-driven training of neural networks to enhance model applicability. Incorporating offline-trained DeepONets to predict actuator dynamics significantly lowers the online computation cost when compared to the existing PINN framework. To address the re-training burden typical of PINNs under varying input conditions, we propose two transfer learning (TL) strategies: (i) a multi-stage TL scheme offering better runtime efficiency than full online training of the PINN model and (ii) a few-shot TL scheme that freezes a shared multi-head network body and computes physics-based derivatives required for model training outside the training loop. The second strategy offers a computationally inexpensive and physics-based approach for predicting engine dynamics and parameter identification, offering computational efficiency over the existing PINN framework. Compared to existing health monitoring methods, our framework combines the interpretability of physics-based models with the flexibility of deep learning, offering substantial gains in generalization, accuracy, and deployment efficiency for diesel engine diagnostics.

💡 Research Summary

The paper presents a novel hybrid digital‑twin framework for system‑level health monitoring of diesel engines that fuses Physics‑Informed Neural Networks (PINNs) with Deep Operator Networks (DeepONet) and augments them with two transfer‑learning (TL) strategies. Traditional data‑driven neural‑network approaches for engine diagnostics are often limited to component‑level analysis, lack interpretability, and suffer from poor generalization outside the training regime. Conversely, pure physics‑based methods such as extended Kalman filters or PINNs provide interpretability but are computationally intensive, especially when the model must be retrained for each new operating condition.

To overcome these shortcomings, the authors first embed the mean‑value diesel engine model (a set of differential equations describing torque, fuel flow, exhaust gas recirculation, etc.) into a PINN loss function. The PINN simultaneously learns unknown system parameters (e.g., injector delay, EGR flow coefficient) and the state trajectories that satisfy the governing equations. However, PINNs require the independent state variables at each time step, which would normally be obtained by solving the full set of equations repeatedly. The authors therefore introduce DeepONet as a fast surrogate operator that maps time‑varying control inputs (fuel injection command, throttle position) to the actuator dynamics (e.g., fuel flow, valve opening). DeepONet is trained offline on a large synthetic dataset generated from the Simulink implementation of the mean‑value model, and once trained it can predict the actuator response in milliseconds, dramatically reducing the online computational burden of the PINN.

Two TL schemes are devised to further cut inference time when the engine operates under new conditions:

1. Multi‑stage Transfer Learning – The full hybrid model (PINN + DeepONet) is first trained on a broad distribution of operating points covering a wide range of loads, speeds, and ambient conditions. When a new scenario appears, only a small subset of parameters (typically the unknown physical coefficients) are fine‑tuned while the bulk of the network weights remain frozen. This yields a 5–10× speed‑up compared with retraining the entire PINN from scratch.

2. Few‑shot Transfer Learning with a Multi‑head Architecture – A large pre‑trained backbone with multiple output heads is kept fixed; a new head is added for the specific scenario and trained on a handful of data points (few‑shot). Crucially, the physics‑based loss gradients (required for the PINN) are computed once outside the training loop and stored, so the few‑shot adaptation does not need to recompute costly automatic‑differentiation steps. This results in sub‑millisecond parameter updates (≈0.005 s) and minimal GPU memory usage.

The authors validate the approach on three test cases derived from the mean‑value model: (i) nominal operation, (ii) a shift in fuel‑injection timing, and (iii) a variation in EGR flow. Synthetic measurement data are corrupted with Gaussian noise to emulate real‑world sensor uncertainty. Compared with a baseline PINN that must be retrained for each case, the hybrid framework reduces the mean absolute error of the identified parameters by more than 30 % and brings the online inference time down to ~0.02 s, satisfying real‑time constraints for on‑engine control units. Both TL strategies achieve comparable accuracy, but the few‑shot method offers the lowest computational overhead.

The paper’s contributions are threefold: (1) a physics‑informed, operator‑infused digital twin that unifies the entire diesel engine system rather than isolated components; (2) two practical TL mechanisms that eliminate the need for full retraining when operating conditions change; and (3) a demonstration that the combined approach retains the interpretability of physics‑based models while delivering the flexibility and speed of deep learning.

Limitations are acknowledged: the DeepONet pre‑training requires extensive simulated data, and the current validation relies on synthetic data augmented with noise rather than large‑scale field trials. Future work will focus on deploying the framework on actual engine test‑beds and extending the operator to handle multi‑modal sensor streams (vibration, acoustic, and emissions).

In summary, by marrying PINNs, DeepONet, and transfer learning, the authors deliver a computationally efficient, accurate, and physically consistent digital twin capable of real‑time parameter identification and health monitoring for diesel engines, marking a significant step forward over existing model‑based or pure data‑driven diagnostic techniques.