STFM: A Spatio-Temporal Information Fusion Model Based on Phase Space Reconstruction for Sea Surface Temperature Prediction

TL;DR

This work addresses SST forecasting by treating SST as a nonlinear dynamical system and applying phase-space reconstruction to form attractors from multivariate histories. It introduces a Spatio-Temporal Information Transformation (STI) and a neural Spatio-Temporal Fusion Model (STFM), with the STFM-V1 variant incorporating Self-Attention, normalization, residuals, a baseline reference, and diagonal-consistency loss to robustly map the initial attractor to the delayed attractor. Across NOAA OISST v2.1 data, STFM-V1 achieves superior short- to mid-term SST predictions compared with LSTM, XGBoost, DNN, and persistence, while maintaining stability across spatial scales and seasons. Limitations include neglecting external forcings; future directions include incorporating winds and currents, time-position embeddings, and self-supervised learning for broader applicability such as turbulence prediction.

Abstract

The sea surface temperature (SST), a key environmental parameter, is crucial to optimizing production planning, making its accurate prediction a vital research topic. However, the inherent nonlinearity of the marine dynamic system presents significant challenges. Current forecasting methods mainly include physics-based numerical simulations and data-driven machine learning approaches. The former, while describing SST evolution through differential equations, suffers from high computational complexity and limited applicability, whereas the latter, despite its computational benefits, requires large datasets and faces interpretability challenges. This study presents a prediction framework based solely on data-driven techniques. Using phase space reconstruction, we construct initial-delay attractor pairs with a mathematical homeomorphism and design a Spatio-Temporal Fusion Mapping (STFM) to uncover their intrinsic connections. Unlike conventional models, our method captures SST dynamics efficiently through phase space reconstruction and achieves high prediction accuracy with minimal training data in comparative tests

Figures (14)

• Figure 1: Discrete sampling of sea surface temperature.
• Figure 2: Two different variable association options. The yellow rectangle represents the area to be predicted. Within this region, for any fixed grid point, the red sliding rectangle centered at the target variable location contains the grid points to be associated with the variable.
• Figure 3: The overall model architecture is shown, including the layout of the seasonal and trend mapping modules, and the process of obtaining delayed attractors through the time-space aggregation module.
• Figure 4: Demonstrates the overall architecture of the single-step mapping $\varphi$ for the initial attractor $O$. First, the input data is processed using the sliding window method to extract local trend features, and the trend decomposition module $\text{Trend}$ extracts the trend information $T$ from the time series. The obtained trend features are then processed through multiple layers of fully connected layers to capture long-term dependencies, ultimately generating the trend prediction matrix $F$.
• Figure 5: Demonstrates the single-step mapping for the univariate initial attractor $x_{i}^{M} = \left[ x_{i}(t_{1}), x_{i}(t_{2}), \dots, x_{i}(t_{M}) \right]$ and the overall mapping structure of $X^{T}$. First, the input data is processed using the sliding window method to extract local seasonal features, and the seasonal decomposition module $\text{Season}$ extracts the seasonal information $S$ from the time series. The obtained seasonal features are then processed through multiple layers of fully connected layers to further mine the periodic variations in the seasonal features, ultimately generating the seasonal prediction matrix $G$.