Physics-Informed Depth-Conditional Neural Network for Chlorophyll-a Profile Reconstruction and Uncertainty Quantification

Accurate reconstruction of vertical chlorophyll-a (Chla) profiles is essential for understanding phytoplankton distribution, evaluating primary productivity, and constraining the marine carbon cycle. However, sparse in situ observations and the complexity of physical–biological interactions make it difficult to infer full-depth Chla structures from surface data. Existing observation-, model-, and hybrid-driven approaches trade off between physical interpretability and adaptability, while purely data-driven models often lack physical consistency and perform poorly under domain shifts. To overcome these limitations, this study proposes a zero-shot cross-domainDeep Conditional Neural Function Generator(DCNFG). The model explicitly incorporates depth as a continuous conditioning variable, applies Feature-wise Linear Modulation (FiLM) to couple surface environmental factors with depth-dependent features, and integrates heteroscedastic and quantile regression for comprehensive uncertainty quantification. Physical regularizations, including smoothness, unimodality, and curvature constraints, are introduced to ensure ecological and optical consistency. Extending the evaluation beyond the Mediterranean and Black Seas, cross-domain experiments in the Subpolar North Atlantic and the Labrador Sea further confirm that DCNFG consistently outperforms baseline models in terms of Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Squared Error (MSE), and profile-wise correlation(R2). The model maintains high structural fidelity and stable uncertainty coverage under distribution shifts. The results indicate that DCNFG achieves a unified balance between physical consistency, interpretability, and adaptability, providing a robust framework for reliable and generalizable reconstruction of oceanic Chla profiles.