The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods.

Future Cooperative Intelligent Transport Systems (C-ITSs) will impose stringent requirements on mobile networks in terms of latency, data rate, and reliability. These requirements must be met in rapidly changing wireless channel conditions. Hence, their fulfillment requires rigorous and reproducible testing environments that enable a seamless transition from simulation to real-world deployment. However, existing testbeds and simulation environments either lack physical realism or fail to scale cost-effectively, hindering comprehensive C-ITS evaluation. To overcome these limitations, we implement the concept of a Digital Triplet, comprising three complementary layers: a full-scale real-world test field, a co-simulation environment for integrating additional simulated entities, and a scaled-down replica of the test field. This architecture enables reliable, reproducible, and scalable testing of future 6G-enabled C-ITS applications across different levels of abstraction. We demonstrate the applicability of the Digital Triplet through multiple case studies. For remote driving, we deploy and optimize a low-latency video streaming system and simulate a mmWave communication channel incorporating Reconfigurable Intelligent Surfaces (RISs), and achieve up to a 74% reduced median Glass-To-Glass (G2G) latency compared to related work. Moreover, emulating real-world vehicle localization in the scaled test field enables the implementation of cross-domain Nonlinear Model Predictive Control (NMPC)-based vehicular platooning. Finally, we evaluate the NMPC platooning controller in both decentralized (on-vehicle) and centralized (edge cloud) configurations. The results highlight the strong potential of the Digital Triplet to accelerate the development and validation of C-ITS applications within future 6G networks.