SSTODE: Ocean-Atmosphere Physics-Informed Neural ODEs for Sea Surface Temperature Prediction

TL;DR

SSTODE, a physics-informed Neural Ordinary Differential Equations (Neural ODEs) framework for SST prediction, derives ODEs from fluid transport principles, incorporating both advection and diffusion to model ocean spatiotemporal dynamics, and introduces an Energy Exchanges Integrator-inspired by ocean heat budget equations-to account for external forcing factors.

Abstract

Sea Surface Temperature (SST) is crucial for understanding upper-ocean thermal dynamics and ocean-atmosphere interactions, which have profound economic and social impacts. While data-driven models show promise in SST prediction, their black-box nature often limits interpretability and overlooks key physical processes. Recently, physics-informed neural networks have been gaining momentum but struggle with complex ocean-atmosphere dynamics due to 1) inadequate characterization of seawater movement (e.g., coastal upwelling) and 2) insufficient integration of external SST drivers (e.g., turbulent heat fluxes). To address these challenges, we propose SSTODE, a physics-informed Neural Ordinary Differential Equations (Neural ODEs) framework for SST prediction. First, we derive ODEs from fluid transport principles, incorporating both advection and diffusion to model ocean spatiotemporal dynamics. Through variational optimization, we recover a latent velocity field that explicitly governs the temporal dynamics of SST. Building upon ODE, we introduce an Energy Exchanges Integrator (EEI)-inspired by ocean heat budget equations-to account for external forcing factors. Thus, the variations in the components of these factors provide deeper insights into SST dynamics. Extensive experiments demonstrate that SSTODE achieves state-of-the-art performances in global and regional SST forecasting benchmarks. Furthermore, SSTODE visually reveals the impact of advection dynamics, thermal diffusion patterns, and diurnal heating-cooling cycles on SST evolution. These findings demonstrate the model's interpretability and physical consistency.

Figures (4)

• Figure 1: Two primary mechanisms govern SST variability (red: warming, blue: cooling): internal ocean dynamics (coupled advection-diffusion dynamics) and external energy exchanges. Among them, thermal diffusion is particularly crucial since it models heat spread driven by seawater movements like subgrid-scale eddies (see zoomed-in box), and coastal upwelling due to boundary effects (see black arrows). External energy exchanges mainly include shortwave radiation (SW), longwave radiation (LW), sensible heat flux (SHF), and latent heat flux (LHF).
• Figure 2: SSTODE framework. It comprises three modules: (1) Initial Velocity Estimation infers latent initial velocity from past SST by solving a PDE-constrained inverse problem; (2) SST-ODE integrates the advection–diffusion equation using Neural ODEs to prediction SST and latent velocity over continuous time; and (3) Energy Exchange Integrator (EEI) refines predictions using surface heat flux data via a learned source network. Spatiotemporal Embeddings (ST Embedding) encode position and time context. $\otimes$: concatenation. $\oplus$: element-wise addition.
• Figure 3: Visualization of intermediate dynamics across three time steps ($t$ = 1 to 3). Rows show: Ground-truth SST, SST Variation, Advection, Diffusion, Velocity Field, and Source Term. SSTODE decouples these components, yielding interpretable and physically grounded results across the forecast horizon.
• Figure 4: Impact of diffusion modeling on prediction bias. Left to right: SST variation, learned diffusion term with strong coastal responses, prediction bias without diffusion, and reduced bias with diffusion, especially in the red box.