# Learning more physically realistic dynamics in machine-learning based weather forecasting with latent-space constraints

arXiv: https://arxiv.org/abs/2510.04006 · HTML: https://mlsanity.com/paper/2510.04006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [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)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [GraphDOP: Towards skilful data-driven medium-range weather forecasts learnt and initialised directly from observations](https://mlsanity.com/paper/2412.15687/) (2024)
- [Global atmospheric data assimilation with multi-modal masked autoencoders](https://mlsanity.com/paper/2407.11696/) (2024)
- [Generating Unseen Nonlinear Evolution in Sea Surface Temperature Using a Deep Learning-Based Latent Space Data Assimilation Framework](https://mlsanity.com/paper/2412.13477/) (2024)

## Built on by (most cited first, 1 of 1)

- [Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification](https://mlsanity.com/paper/2603.04395/) (2026)

## Abstract (arXiv)

Data-driven machine learning (ML) models are reshaping weather forecasting and have shown the potential to accelerate and surpass traditional physics-based approaches, leading to a second revolution in the field after data assimilation. However, most ML forecast models are trained with weighted variable-wise losses on rollout forecasts that neglect cross-variable and spatial error covariance induced by physical coupling, often yielding overly smooth and physically unrealistic long-range forecasts. To address this, we reformulate model training as a four-dimensional variational data assimilation (4DVar) problem that treats reanalysis data as imperfect observations. This enables the loss function to incorporate cross-variable error covariance structures that capture multivariate dependencies and their associated errors. In practice, we approximate this objective by computing the loss in an autoencoder-learned latent space of global atmospheric states. By encoding complex nonlinear couplings among atmospheric variables, this representation allows the high-dimensional, complex error covariance matrix in model space to be approximated as nearly diagonal in latent space, substantially simplifying implementation. We show that rollout training with latent-space constraints improves long-term forecast skill, while better preserving fine-scale structures and physical realism than the widely used model-space loss. Finally, we extend this framework to accommodate heterogeneous data sources, enabling the forecast model to be trained jointly on reanalysis and multi-source observations within a unified theoretical formulation.