Process-Inspired Latent Dynamics for Direct Multi-Step Regional Sea Surface Temperature Forecasting

Sea surface temperature (SST) forecasts support marine environmental monitoring, hazard assessment, and operational ocean services. Regional multi-step prediction remains difficult because SST-only models must represent transport, spatial spreading, and local nonlinear variation from historical fields while avoiding the recursive use of predicted states. We propose ADR-Net, a direct multi-step forecasting model that combines a flexible data-driven stream with a process-inspired advection–diffusion–reaction (ADR) stream in a shared latent bottleneck. The ADR stream organizes latent SST evolution through three operators that represent transport-like displacement, spatial spreading, and local nonlinear variation. A temporal projection module (TPM) then projects the fused latent representation and multi-scale encoder features directly to all forecast leads. We evaluated ADR-Net against eight learned baselines and two non-learned references using daily OISST v2.1 data from the East China Sea (ECS), South China Sea (SCS), Niño 1+2, and Niño 3.4 regions. Separate models were trained with output lengths L∈{1,7,13}. ADR-Net achieved the lowest MSE, MAE, and RMSE in all 12 region–output length settings across four regions and three output lengths. In the ECS, it reduced the MSE by 1.46%, 8.07%, and 5.70% relative to the best MSE baseline for L=1, L=7, and L=13, respectively. For the ECS L=13 task, ADR-Net maintained the lowest MAE and highest SSIM at every lead day and extended the mean effective forecast horizon from 3.91 to 4.49 days under grid cell thresholds of RMSE ≤ 0.7 °C and R2≥0.95. Component ablations on the ECS seven-day task showed that removing the TPM or the process-inspired ADR stream increased the mean MSE by 4.55% and 3.86%, respectively, while removing both increased it by 8.32%. ADR-Net used 7.09 million parameters and 13.07 GFLOPs per ECS seven-day forecast sample. Across four storm-associated episodes, ADR-Net achieved the lowest event-mean cooling footprint MAE at every forecast lead from day 1 to day 13. Together, these results support the combination of process-inspired latent modeling and direct temporal projection for accurate, spatially coherent regional SST forecasting.