# FlowCast-ODE: Continuous Hourly Weather Forecasting with Dynamic Flow Matching and ODE Solver

arXiv: https://arxiv.org/abs/2509.14775 · HTML: https://mlsanity.com/paper/2509.14775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Scaling transformer neural networks for skillful and reliable medium-range weather forecasting](https://mlsanity.com/paper/2312.03876/) (2023)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting](https://mlsanity.com/paper/2410.03229/) (2024)
- [Improving Global Weather and Ocean Wave Forecast with Large Artificial Intelligence Models](https://mlsanity.com/paper/2401.16669/) (2024)
- [Community Research Earth Digital Intelligence Twin (CREDIT)](https://mlsanity.com/paper/2411.07814/) (2024)

## Built on by (most cited first, 2 of 2)

- [FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matching](https://mlsanity.com/paper/2602.06800/) (2026)
- [SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs](https://mlsanity.com/paper/2610.03313/) (2026)

## Abstract (arXiv)

Data-driven hourly weather forecasting models often face the challenge of error accumulation in long-term predictions. The problem is exacerbated by non-physical temporal discontinuities present in widely-used training datasets such as ECMWF Reanalysis v5 (ERA5), which stem from its 12-hour assimilation cycle. Such artifacts lead hourly autoregressive models to learn spurious dynamics and rapidly accumulate errors. To address this, we introduce FlowCast-ODE, a novel framework that treats atmospheric evolution as a continuous flow to ensure temporal coherence. Our method employs dynamic flow matching to learn the instantaneous velocity field from data and an ordinary differential equation (ODE) solver to generate smooth and temporally continuous hourly predictions. By pre-training on 6-hour intervals to sidestep data discontinuities and fine-tuning on hourly data, FlowCast-ODE produces seamless forecasts for up to 120 hours with a single lightweight model. It achieves competitive or superior skill on key meteorological variables compared to baseline models, preserves fine-grained spatial details, and demonstrates strong performance in forecasting extreme events, such as tropical cyclone tracks.