DP-Twin: A Data–Physics-Driven Method for Modeling Physical Twins of Industrial Cyber-Physical Systems

With the increasing prevalence of sophisticated and stealthy cyber–physical attacks such as covert sensor tampering in industrial cyber-physical systems (ICPS), high-precision physical process modeling has become essential for accurate anomaly detection and other critical security defense tasks. To address this challenge, this paper proposes a data-physics–driven physical twin (DP-Twin) modeling that integrates partial differential equation–based physical constraints with physics-informed neural networks (PINNs), enabling a unified framework that fuses physical priors with data-driven learning. A shared temporal feature extractor is employed to capture common dynamics across multiple operating conditions, while lightweight PINN branches concurrently predict physical states and their derivatives. Furthermore, transfer learning is used to fine-tune the models, thereby reducing training costs and enhancing model generalization capability. When deployed for security monitoring in water treatment systems, DP-Twin leverages physics-consistency constraints to accurately detect abnormal behaviors. Experimental results demonstrate that DP-Twin maintains high predictive accuracy, exhibits strong robustness against noisy measurements, and provides reliable performance under out-of-distribution scenarios. In an industrial anomaly detection task, DP-Twin achieves a precision of 96.21%, highlighting its practical potential for ICPS security monitoring.