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

TL;DR

FlowCast-ODE tackles error accumulation in hourly weather forecasting by addressing assimilation-induced discontinuities in ERA5 data. It treats atmospheric evolution as a continuous flow, learning a velocity field via dynamic flow matching and integrating it with an ODE solver, with a two-stage training strategy that first pre-trains on 6-hour intervals and then fine-tunes on hourly data. The approach yields temporally coherent forecasts up to $120$ hours, preserves fine-scale spatial structure, and matches or exceeds baselines in key variables and tropical cyclone tracking, while reducing artifacts at assimilation boundaries. This continuous-dynamics framework improves forecast stability, spectral fidelity, and operational potential for data-driven, hourly weather prediction, with clear directions for higher resolution, ensemble extensions, and multi-scale design in future work.

Abstract

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.

Figures (9)

• Figure 1: FlowCast-ODE: A continuous-time framework for stable hourly weather forecasting. This figure details FlowCast-ODE's motivation, performance, and methodology. a Discontinuities in ERA5 Hourly Data. ERA5, a foundational training dataset for data-driven weather models, exhibits systemic, non-physical temporal jumps (e.g., in kinetic energy) at the 12-hour data assimilation boundaries (09 and 21 UTC). These artifacts mislead hourly autoregressive models, causing inconsistent physical dynamics and cumulative forecast errors. Most data-driven models, operating on 6-hour intervals (deep blue dots), often unintentionally bypass this critical discontinuity issue. b Continuous Hourly Forecast. A 120-hour forecast of kinetic energy demonstrates that FlowCast-ODE (red, ours) produces remarkably smooth and temporally coherent predictions, outperforming both the fluctuating Pangu-Weather baseline (green) and the original ERA5 data (light blue). c FlowCast-ODE Framework. A two-stage training process to achieve temporally continuous hourly weather forecasting on discontinuous data. First, the velocity field, $v_\theta(x_t, t)$, is learned on 6-hour intervals using a linearized Dynamic Transport path, to continuously transform an initial atmospheric state $X_k$ into target $X_{k+6}$. By training on 6-hour interval data, FlowCast-ODE inherently reduces the impact of these discontinuities. Subsequently, the model is finetuned on hourly data, where an Euler ODE solver integrates the learned dynamics in hourly steps $(X_k \to X_{k+1}, \ldots, X_{k+6})$, yielding stable hourly predictions. For long-range prediction, the solver performs an hourly rollout within 6-hour intervals, with the final state of each interval serving as the initial condition for the next, thus extending the forecast horizon autoregressively.
• Figure 1: Time series of four atmospheric energy components derived from ERA5 data.a internal energy, b latent heat energy, c potential energy, and d kinetic energy. Triangles indicate values at 09 UTC, while square boxes represent values at 21 UTC, highlighting the discontinuities in the dataset.
• Figure 2: Comparison of latitude-weighted global mean RMSE of ClimODE (gray x markers), Pangu-Weather (24-hour intervals, purple dashed line), and FlowCast-ODE (hourly resolution, green line) across a 5-day forecast horizon. Results are shown for four surface variables (MSLP, U10M, T2M, and TD2M) and four upper-air variables (Z500, U850, T850, and Q850). The hourly RMSE of FlowCast-ODE reveals faster error growth around 09:00–10:00 UTC and 21:00–22:00 UTC, reflecting the impact of ERA5’s discontinuities at the boundaries of the 12-hour assimilation windows on the hourly model’s forecast accuracy.
• Figure 2: Validation loss curves (a) and model parameters (b) for FlowCast-ODE using adaLN-Zero temporal modulation with and without Low-Rank decomposition. Both models are trained on ERA5 data from 2010–2019, and the curves are shown across training epochs.
• Figure 3: Latitude-averaged power spectra from 60$^\circ$S to 60$^\circ$N for ERA5 (black line), Pangu-Weather forecasts (purple dashed line), and FlowCast-ODE forecasts (green dashed line). Rows 1, 2, and 3 correspond to forecast days 1, 3, and 5, respectively.