Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bridging the Gap Between Bayesian Deep Learning and Ensemble Weather Forecasts

Xinlei Xiong, Wenbo Hu, Shuxun Zhou, Kaifeng Bi, Lingxi Xie, Ying Liu, Richang Hong, Qi Tian

TL;DR

This work targets uncertainty quantification in weather forecasting by bridging Bayesian deep learning (BDL) with traditional ensemble prediction systems. It introduces a hybrid framework that simultaneously models epistemic uncertainty via variational inference on model parameters and aleatoric uncertainty through a physics-informed, flow-dependent perturbation of the atmospheric state using a spherical-harmonic random field. The approach is underpinned by theoretical results that decompose total predictive uncertainty into its epistemic and aleatoric components and validated on the ERA5 reanalysis dataset, showing improved probabilistic skill, better calibration, and substantial computational efficiency over diffusion-based baselines. The combination yields a practical, scalable method for trustworthy AI-based weather prediction with an actionable open-source direction for operational use.

Abstract

Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally intensive simulations, recent advances in Bayesian Deep Learning (BDL) offer a promising but often disconnected alternative. We bridge these paradigms through a unified hybrid Bayesian Deep Learning framework for ensemble weather forecasting that explicitly decomposes predictive uncertainty into epistemic and aleatoric components, learned via variational inference and a physics-informed stochastic perturbation scheme modeling flow-dependent atmospheric dynamics, respectively. We further establish a unified theoretical framework that rigorously connects BDL and EPS, providing formal theorems that decompose total predictive uncertainty into epistemic and aleatoric components under the hybrid BDL framework. We validate our framework on the large-scale 40-year ERA5 reanalysis dataset (1979-2019) with 0.25° spatial resolution. Experimental results show that our method not only improves forecast accuracy and yields better-calibrated uncertainty quantification but also achieves superior computational efficiency compared to state-of-the-art probabilistic diffusion models. We commit to making our code open-source upon acceptance of this paper.

Bridging the Gap Between Bayesian Deep Learning and Ensemble Weather Forecasts

TL;DR

This work targets uncertainty quantification in weather forecasting by bridging Bayesian deep learning (BDL) with traditional ensemble prediction systems. It introduces a hybrid framework that simultaneously models epistemic uncertainty via variational inference on model parameters and aleatoric uncertainty through a physics-informed, flow-dependent perturbation of the atmospheric state using a spherical-harmonic random field. The approach is underpinned by theoretical results that decompose total predictive uncertainty into its epistemic and aleatoric components and validated on the ERA5 reanalysis dataset, showing improved probabilistic skill, better calibration, and substantial computational efficiency over diffusion-based baselines. The combination yields a practical, scalable method for trustworthy AI-based weather prediction with an actionable open-source direction for operational use.

Abstract

Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally intensive simulations, recent advances in Bayesian Deep Learning (BDL) offer a promising but often disconnected alternative. We bridge these paradigms through a unified hybrid Bayesian Deep Learning framework for ensemble weather forecasting that explicitly decomposes predictive uncertainty into epistemic and aleatoric components, learned via variational inference and a physics-informed stochastic perturbation scheme modeling flow-dependent atmospheric dynamics, respectively. We further establish a unified theoretical framework that rigorously connects BDL and EPS, providing formal theorems that decompose total predictive uncertainty into epistemic and aleatoric components under the hybrid BDL framework. We validate our framework on the large-scale 40-year ERA5 reanalysis dataset (1979-2019) with 0.25° spatial resolution. Experimental results show that our method not only improves forecast accuracy and yields better-calibrated uncertainty quantification but also achieves superior computational efficiency compared to state-of-the-art probabilistic diffusion models. We commit to making our code open-source upon acceptance of this paper.

Paper Structure

This paper contains 27 sections, 4 theorems, 48 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Pre-training deterministic forecasting model
  5. Epistemic Uncertainty
  6. Aleatoric Uncertainty
  7. Combing two uncertainties in one model
  8. Experiments
  9. Setups
  10. Ensemble skill
  11. Ensemble calibration
  12. Computational efficiency
  13. Ablation Study
  14. Conclusion
  15. Proof and derivation details
  16. ...and 12 more sections

Key Result

Theorem 1

Let $X_{t-1:t}$ be a deterministic scalar field defined on the sphere $S^2$ of radius $R$. Let $r_t(s)$ be a zero-mean, statistically isotropic Gaussian random field on $S^2$ with angular power spectrum $C_l=\kappa^2(\frac{l(l+1)}{R^2} +\tau ^2)^{-\gamma }$ for $l\ge 1$, with $C_0=0$. Consider the m 3) Spatial covariance: For any two locations $s_u,s_v \in S^2$ with angular distance $\gamma_{uv}$:

Figures (12)

  • Figure 1: Visualization of 1 day, 3 day, 10 day and 15 day weather forecasting of our method, combing two uncertainties. Validation start date is 06:00 UTC, October 6, 2018. The left panel shows the initial conditions and forecast area. The right panel displays the forecasts of selected ensemble members compared with Ground Truth.
  • Figure 1: Visualisation of Geopotential at 500 hPa.
  • Figure 2: Overview of the proposed workflow. (a) Pre-training phase: the model learns a deterministic mapping from inputs to outputs;(b) Post-training phase: the pre-trained weights are loaded to perform posterior distribution learning for quantifying epistemic uncertainty; (c)Autoregressive inference phase: initialize $M$ ensemble models and introduce perturbations to simulate aleatoric uncertainty.
  • Figure 2: Visualisation of Specific humidity at 925 hPa.
  • Figure 3: Predicted Mean sea level pressure with a 24-hour lead time, validation start date is 06:00 UTC, January 1, 2018.
  • ...and 7 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2: Decomposition of Predictive Uncertainty
  • Theorem 1
  • Theorem 2: Decomposition of Predictive Uncertainty