Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data

Data and physics requirements for reliable physics‐informed neural networks in process modeling

Physics‐informed neural networks (PINNs) have gained increasing attention in chemical process modeling since they can embed first‐principles knowledge into neural network training. However, in practice, the embedded physics is often inaccurate, and experimental data are costly to obtain, raising fundamental questions about the required physics‐model accuracy and data volume required to achieve a target prediction accuracy. This work develops a theoretical framework for analyzing the generalization error of PINNs under model misspecification. We establish both an architecture‐independent error bound and an explicit bound for a specific PINN architecture. The bound is further related to the solution error with respect to the true system, yielding quantitative conditions on admissible model discrepancy, data requirements, and loss‐weight selection. Based on these conditions, two adaptive algorithms are proposed to guide physics‐model refinement and data collection. The theoretical findings are demonstrated using a chemical process network.

From Newton to Neural Networks: A Review of Data-Driven Physical Modelling and the Rise of Physics-Informed AI

This review examines the evolution of physical modelling from classical first-principles approaches to contemporary data-driven and physics-informed learning frameworks, with a central focus on Physics-Informed Neural Networks and related hybrid methods that integrate governing laws into learning algorithms to improve prediction, generalization, and physical plausibility.

A parameterized learning method based on data-driven and physical constraints for solving the fluid model of low-temperature plasma

Low-temperature plasma (LTP) plays an indispensable role in environmental remediation and energy conversion. Rapid prediction of state parameters in LTP is crucial for enhancing both pollutant degradation efficiency and fuel conversion performance. To address the high computational cost of traditional numerical methods for LTP modeling, this research proposes a coupled physics-driven and data-driven approach incorporating parameterized learning. This approach introduces applied voltage as an input parameter while parameterized learning is adopted for rapid prediction of electrostatic potential and charged particle densities in LTP. Meanwhile, optical sensing technology is employed to high-fidelity measurement of potential for model validation. The results demonstrate that the method effectively captures the distribution features of electrostatic potential and charged particles in LTP. The trained model can generate prediction results within 1 s, achieve an average relative L2 error (RL2E) of 8.72 × 10−3 and mean absolute error of 4.39 V. This study confirms the feasibility of physics-informed approaches in advancing LTP modeling, offering a pathway toward efficient approach for the online condition assessment and multi-parameter optimization design of plasma devices.

Probabilistic Physics-Aware Machine Learning Predictions of Electric Truck Energy Consumption with Field Data

In this work, we incorporate first principle physics into the construction of data-driven methods by considering a model that accounts for the different sources of energy losses during vehicle operations. Our results show that Bayesian linear regression based on this physics-aware model can improve the reliability of the expected energy consumption, as compared with standard linear regression. Further, it is shown that more complex machine learning models such as neural networks and gradient boosted regression trees, based on the same physical model, can further improve the accuracy in energy forecasting and significantly outperform standard versions of the same machine learning models. In addition to point predictions of the energy consumption, we develop a framework for estimating the corresponding uncertainty in the form of predicted standard deviation. Our results show that all of the models learn to estimate the uncertainty reasonably well.

Physics-Informed Impact Identification (Phy-ID): Combining Physics and Data for Structural Health Monitoring of Aerospace Composites

This paper presents the Physics-Informed Impact Identification (Phy-ID) framework. It addresses the challenges of reconstructing impact parameters from passive sensor signals. Phy-ID integrates physical knowledge into machine learning across three complementary levels: how data representation is defined, how the model is built, and how optimisation is guided. Each level is described conceptually and illustrated with documented examples from previous work of the authors and the literature. Examples cover both established strategies and new directions yet to be applied to impact identification. By aligning model design with prior knowledge of composite structures under impact, Phy-ID provides a structured, scalable modelling approach. It targets improved robustness, interpretability, and generalisation in conditions of partial physical knowledge and limited experimental data, which are typical in real-world SHM.

Machine learning based radiation emulation: development and performance evaluation in operational reforecast experiments