A physics-constrained neural operator for state reconstruction and real-time parameter identification in industrial fluid-network digital twins

Real-time digital twins of industrial fluid networks are challenged by sparse sensing and time-varying equipment parameters, which together create a severely ill-posed joint state-parameter inverse problem. To address this issue, this paper proposes a cascaded physics-constrained neural operator (PC-NO) that decomposes the original problem into two sequential subtasks: plant-wide state reconstruction and component-level parameter identification. For front-end state reconstruction, a physics-consistent graph neural network (PC-GNN) is developed to map sparse observations onto a graph state with pressure-subspace consistency enforced through a Kirchhoff hard-constraint projection layer. For back-end parameter identification, a stable window-attentive physics-informed neural network (SWA-PINN) is developed to perform fast and robust online parameter estimation through time-domain cumulative optimization, dynamic-static separation, and an analytical Jacobian that replaces repeated AutoDiff-based gradient evaluation in the online update stage. Evaluations based on real SCADA data show that, under an extreme 40% pressure-masking rate, PC-GNN reduces the mean mass balance residual (MMBR) by 69.2% and the reconstruction RMSE by 42.5% relative to the strongest data-driven baseline. Meanwhile, SWA-PINN achieves transient zero-lag tracking during operating-mode switching and delivers a nearly 19-fold inference acceleration over the AutoDiff-based baseline. Overall, PC-NO provides a computationally tractable route for plant-wide state estimation and online equipment monitoring in industrial energy/process facilities.