Leveraging Generative Models for Uncertainty-Aware Sea Waves 3-D Reconstruction

In this paper we investigate a generative AI approach for interpolating 3D point clouds of sea surface elevation data.Unlike classic AI models, which aim to reconstruct a dense surface directly from scattered samples, we leverage denoising diffusion probabilistic models (DDPMs) to cast the interpolation as the problem of stochastically generating realistic surfaces loosely constrained to the available points. Such a process exploits a neural model trained to discriminate noise from the underlying wave elevation signal to iteratively and gradually remove noise from an initial random scalar field. Different random fields generate alternative reconstructions from the same sparse set of points, all exhibiting realistic spectra — especially at high wavenumbers — overcoming the Shannon–Nyquist sampling rate theoretical lower bound.We observed that the standard deviation of the generated sea surface elevations (at each grid point) strongly correlates with the mean absolute error against the true surface elevation, providing an inherent uncertainty quantification metric. This correlation offers a dual benefit: it provides a reliable assessment of the model's performance in regions with sparse data and a way to fuse temporally related reconstructions by weighting the dispersion relation constraint with the generated surface fields.Our experiments show that the proposed method offers an improvement with respect to traditional interpolation techniques, considering the fidelity to the ground truth surface, computational efficiency, and the ability to quantify uncertainty.