Physics-Informed Residual Neural Ordinary Differential Equations for Enhanced Tropical Cyclone Intensity Forecasting

TL;DR

The paper tackles tropical cyclone intensity forecasting by introducing a Physics-Informed Residual Neural Ordinary Differential Equation (PIR-NODE) that models TC evolution as a continuous-time dynamical system. It fuses Neural ODEs with residual connections and physics-informed inputs to improve predictive accuracy and stability on the SHIPS dataset, formulating the dynamics with $\frac{dx(t)}{dt}=f(x(t), t; \theta)$. The approach achieves substantial gains over traditional models and baselines, reporting RMSE of $10.40$ kt and $R^2=0.847$ for 24-hour forecasts, with a 25.2% RMSE reduction and 19.5% R^2 increase relative to a neural network baseline, while preserving initial state information and generalizing across basins. The work demonstrates the potential of physics-informed, continuous-time deep learning for geophysical prediction and lays groundwork for multi-modal data fusion, uncertainty quantification, and real-time operational forecasting.

Abstract

Accurate tropical cyclone (TC) intensity prediction is crucial for mitigating storm hazards, yet its complex dynamics pose challenges to traditional methods. Here, we introduce a Physics-Informed Residual Neural Ordinary Differential Equation (PIR-NODE) model to precisely forecast TC intensity evolution. This model leverages the powerful non-linear fitting capabilities of deep learning, integrates residual connections to enhance model depth and training stability, and explicitly models the continuous temporal evolution of TC intensity using Neural ODEs. Experimental results in the SHIPS dataset demonstrate that the PIR-NODE model achieves a significant improvement in 24-hour intensity prediction accuracy compared to traditional statistical models and benchmark deep learning methods, with a 25. 2\% reduction in the root mean square error (RMSE) and a 19.5\% increase in R-square (R2) relative to a baseline of neural network. Crucially, the residual structure effectively preserves initial state information, and the model exhibits robust generalization capabilities. This study details the PIR-NODE model architecture, physics-informed integration strategies, and comprehensive experimental validation, revealing the substantial potential of deep learning techniques in predicting complex geophysical systems and laying the foundation for future refined TC forecasting research.

Figures (9)

• Figure 1: Physics-Informed Residual Neural Ordinary Differential Equation Model (PIR-NODE) Architecture.
• Figure 2: Internal Structure of the Residual ODE Function.
• Figure 3: Performance by Basin.
• Figure 4: Performance by Storm Category.
• Figure 5: Performance by Seasonal Variation.