Mitigating Time Discretization Challenges with WeatherODE: A Sandwich Physics-Driven Neural ODE for Weather Forecasting

TL;DR

WeatherODE is a physics-driven neural ODE model that improves weather forecasting by addressing time discretization errors and dynamic atmospheric processes through a novel wave equation-based approach and a specialized CNN-ViT-CNN structure.

Contribution

The paper introduces WeatherODE, a new physics-informed neural ODE model with a unique sandwich structure, enhancing weather prediction accuracy over existing methods.

Findings

Outperforms state-of-the-art models by over 40% in global RMSE reduction.

Achieves over 31.8% RMSE improvement in regional weather forecasting.

Effectively mitigates time-discretization errors in weather models.

Abstract

In the field of weather forecasting, traditional models often grapple with discretization errors and time-dependent source discrepancies, which limit their predictive performance. In this paper, we present WeatherODE, a novel one-stage, physics-driven ordinary differential equation (ODE) model designed to enhance weather forecasting accuracy. By leveraging wave equation theory and integrating a time-dependent source model, WeatherODE effectively addresses the challenges associated with time-discretization error and dynamic atmospheric processes. Moreover, we design a CNN-ViT-CNN sandwich structure, facilitating efficient learning dynamics tailored for distinct yet interrelated tasks with varying optimization biases in advection equation estimation. Through rigorous experiments, WeatherODE demonstrates superior performance in both global and regional weather forecasting tasks, outperforming recent state-of-the-art approaches by significant margins of over 40.0\% and 31.8\% in root mean square error (RMSE), respectively. The source code is available at \url{https://github.com/DAMO-DI-ML/WeatherODE}.