Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting

TL;DR

This paper presents PARADIS, a neural weather forecasting architecture that enforces an advection–diffusion–reaction decomposition in latent space and embeds a differentiable Neural Semi-Lagrangian transport operator on the sphere. By learning which latent features to advect and along which trajectories, PARADIS achieves state-of-the-art or competitive forecast skill at 1° resolution with substantially lower training cost compared to 0.25° baselines, while preserving spectral energy and phase information through a three-phase curriculum (reversed Huber loss, autoregressive fine-tuning, and spectral fine-tuning). The approach yields favorable performance across lead times up to 10 days, improves vertical and multiscale structure, and delivers robust cyclone-tracking performance, highlighting the value of explicit transport physics in neural weather prediction. The work also demonstrates how latent-space transport can generalize across scales and geometry, suggesting practical pathways for higher-resolution and probabilistic extensions in operational forecasting.

Abstract

Recent machine-learning approaches to weather forecasting often employ a monolithic architecture, where distinct physical mechanisms (advection, transport), diffusion-like mixing, thermodynamic processes, and forcing are represented implicitly within a single large network. This representation is particularly problematic for advection, where long-range transport must be treated with expensive global interaction mechanisms or through deep, stacked convolutional layers. To mitigate this, we present PARADIS, a physics-inspired global weather prediction model that imposes inductive biases on network behavior through a functional decomposition into advection, diffusion, and reaction blocks acting on latent variables. We implement advection through a Neural Semi-Lagrangian operator that performs trajectory-based transport via differentiable interpolation on the sphere, enabling end-to-end learning of both the latent modes to be transported and their characteristic trajectories. Diffusion-like processes are modeled through depthwise-separable spatial mixing, while local source terms and vertical interactions are modeled via pointwise channel interactions, enabling operator-level physical structure. PARADIS provides state-of-the-art forecast skill at a fraction of the training cost. On ERA5-based benchmarks, the 1 degree PARADIS model, with a total training cost of less than a GPU month, meets or exceeds the performance of 0.25 degree traditional and machine-learning baselines, including the ECMWF HRES forecast and DeepMind's GraphCast.

Figures (28)

• Figure 1: Tracking of cyclone eye for Hurricane Laura (August 2020) using different models and the observed trajectory (IBTrACS dataset knapp2010internationalgahtan2024ibtracs).
• Figure 2: Diagram of the PARADIS model.
• Figure 3: Comparison of implicit vs. explicit advection. An idealized experiment on a $721\times1440$ grid. Top left: Initial Gaussian tracer. Top right: Target state after advection under a spatially uniform wind. Bottom left: Prediction from a UNet of recursive depth 3, with about 44,000 total parameters. The fixed domain of dependence acts as a hard limit on how far information can be transported. Bottom right: Prediction from the Neural Semi-Lagrangian (NSL) layer with only 20 learnable parameters, which accurately relocates the tracer while preserving its structural integrity.
• Figure 4: NSL Advection scheme. The value at the arrival grid point $\mathbf{x}$ () is determined by tracing the trajectory backward to the off-grid departure point $\mathbf{x}_d$ (). The value at $\mathbf{x}_d$ is then computed via interpolation using the surrounding stencil of active grid points.
• Figure 5: Vertical and surface RMSE differences between PARADIS and ECMWF HRES as a function of forecast lead time. Shown are area-weighted RMSE differences (PARADIS minus HRES) for atmospheric variables evaluated across pressure levels. Negative values (blue) indicate lower error for PARADIS relative to HRES. Results demonstrate increasing skill gains for PARADIS with lead time, particularly in the mid- to upper-troposphere and for dynamical variables.