Probabilistic wave field reconstruction via Bayesian Neural Fields

Reliable characterization of wave energy resources is a prerequisite for the sustainable development of the blue economy, yet it remains challenging due to the spatiotemporal sparsity of satellite altimetry and limited in-situ networks. This study introduces a probabilistic data fusion framework based on Bayesian Neural Fields (BayesNF) that reconstructs continuous, high-resolution significant wave height fields with rigorous uncertainty quantification, using only spatiotemporal coordinates as inputs. The framework is trained on a heterogeneous constellation of nine satellite missions covering the North Tyrrhenian Sea and is assessed through a domain-aware validation strategy that separates satellite-based training from independent SWOT altimetry validation and moored-buoy testing. On the independent buoy record, BayesNF attains a mean absolute error of 0.35 m and a root mean square error (RMSE) of 0.50 m, reducing RMSE by approximately 26% relative to the operational CMEMS L4 product (0.68 m) and 24% relative to a deterministic deep-learning baseline of identical capacity (0.66 m), while approaching the accuracy of the physics-based CMEMS Wave Reanalysis (0.31 m) using no meteorological forcing. Unlike these deterministic products, BayesNF delivers calibrated predictive intervals, with an empirical 95% credible-interval coverage of 95.6%. The framework generates a full-month, high-resolution regional wave field in under a minute (roughly 52 s on a single TPU v6e). Finally, we propagate these stochastic reconstructions into continuous maps of wave energy density, demonstrating how the probabilistic approach captures the non-linear amplification of uncertainty and provides transparent bounds that support preliminary, proxy-based screening of offshore renewable energy potential.