Controllable Probabilistic Forecasting with Stochastic Decomposition Layers

• URL: http://arxiv.org/abs/2512.18815v1
• Date: Sun, 21 Dec 2025 17:10:00 GMT
• Title: Controllable Probabilistic Forecasting with Stochastic Decomposition Layers
• Authors: John S. Schreck, William E. Chapman, Charlie Becker, David John Gagne, Dhamma Kimpara, Nihanth Cherukuru, Judith Berner, Kirsten J. Mayer, Negin Sobhani,
• Abstract summary: We introduce Decomposition Layers (SDL) for converting deterministic machine learning weather models into ensemble systems.<n>SDL applies learned perturbations at three decoder scales through latent-driven modulation, per-pixel noise, and channel scaling.<n>When applied to WXFormer via transfer learning, SDL requires less than 2% of the computational cost needed to train the baseline model.
• Score: 1.3995263206621
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less computational cost compared with diffusion-based methods. However, current CRPS ensemble approaches vary in their training strategies and noise injection mechanisms, with most injecting noise globally throughout the network via conditional normalization. This structure increases training expense and limits the physical interpretability of the stochastic perturbations. We introduce Stochastic Decomposition Layers (SDL) for converting deterministic machine learning weather models into probabilistic ensemble systems. Adapted from StyleGAN's hierarchical noise injection, SDL applies learned perturbations at three decoder scales through latent-driven modulation, per-pixel noise, and channel scaling. When applied to WXFormer via transfer learning, SDL requires less than 2\% of the computational cost needed to train the baseline model. Each ensemble member is generated from a compact latent tensor (5 MB), enabling perfect reproducibility and post-inference spread adjustment through latent rescaling. Evaluation on 2022 ERA5 reanalysis shows ensembles with spread-skill ratios approaching unity and rank histograms that progressively flatten toward uniformity through medium-range forecasts, achieving calibration competitive with operational IFS-ENS. Multi-scale experiments reveal hierarchical uncertainty: coarse layers modulate synoptic patterns while fine layers control mesoscale variability. The explicit latent parameterization provides interpretable uncertainty quantification for operational forecasting and climate applications.

Related papers

• Silent Inconsistency in Data-Parallel Full Fine-Tuning: Diagnosing Worker-Level Optimization Misalignment [27.352639822596146]
  Cross-worker divergence in losses and gradients can remain invisible under conventional monitoring signals.<n>We propose a model-agnostic diagnostic framework that quantifies worker-level consistency using training signals readily available in standard pipelines.
  arXiv  Detail & Related papers  (2026-02-16T04:42:30Z)
• RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting [4.140149411004857]
  RDIT is a plug-and-play framework that combines point estimation and residual-based conditional diffusion with a bidirectional Mamba network.<n>We show that RDIT achieves lower CRPS, rapid inference, and improved coverage compared to strong baselines.
  arXiv  Detail & Related papers  (2025-09-02T14:06:29Z)
• Locally Adaptive Conformal Inference for Operator Models [5.78532405664684]
  We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued locally adaptive prediction sets for operator models.<n>We prove finite-sample validity and derive a data-dependent upper bound on the coverage gap under local exchangeability.<n>We empirically demonstrate spaces against biased predictions and certain out-of-distribution noise regimes.
  arXiv  Detail & Related papers  (2025-07-28T16:37:56Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [70.8832906871441]
  We study how to steer generation toward desired rewards without retraining the models.<n>Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement.<n>We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Generative Latent Neural PDE Solver using Flow Matching [8.397730500554047]
  We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space.<n>Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries.<n> Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability.
  arXiv  Detail & Related papers  (2025-03-28T16:44:28Z)
• Gradient Normalization Provably Benefits Nonconvex SGD under Heavy-Tailed Noise [60.92029979853314]
  We investigate the roles of gradient normalization and clipping in ensuring the convergence of Gradient Descent (SGD) under heavy-tailed noise. Our work provides the first theoretical evidence demonstrating the benefits of gradient normalization in SGD under heavy-tailed noise. We introduce an accelerated SGD variant incorporating gradient normalization and clipping, further enhancing convergence rates under heavy-tailed noise.
  arXiv  Detail & Related papers  (2024-10-21T22:40:42Z)
• Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion [56.38386580040991]
  Consistency Trajectory Model (CTM) is a generalization of Consistency Models (CM) CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance. Unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods.
  arXiv  Detail & Related papers  (2023-10-01T05:07:17Z)
• CSQ: Growing Mixed-Precision Quantization Scheme with Bi-level Continuous Sparsification [51.81850995661478]
  Mixed-precision quantization has been widely applied on deep neural networks (DNNs) Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. We propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability.
  arXiv  Detail & Related papers  (2022-12-06T05:44:21Z)
• Probabilistic partition of unity networks: clustering based deep approximation [0.0]
  Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs. We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based generalizations of a maximum likelihood loss. We provide benchmarks quantifying performance in high/low-dimensions, demonstrating that convergence rates depend only on the latent dimension of data within high-dimensional space.
  arXiv  Detail & Related papers  (2021-07-07T08:02:00Z)
• Layer Pruning on Demand with Intermediate CTC [50.509073206630994]
  We present a training and pruning method for ASR based on the connectionist temporal classification (CTC) We show that a Transformer-CTC model can be pruned in various depth on demand, improving real-time factor from 0.005 to 0.002 on GPU.
  arXiv  Detail & Related papers  (2021-06-17T02:40:18Z)
• Probabilistic electric load forecasting through Bayesian Mixture Density Networks [70.50488907591463]
  Probabilistic load forecasting (PLF) is a key component in the extended tool-chain required for efficient management of smart energy grids. We propose a novel PLF approach, framed on Bayesian Mixture Density Networks. To achieve reliable and computationally scalable estimators of the posterior distributions, both Mean Field variational inference and deep ensembles are integrated.
  arXiv  Detail & Related papers  (2020-12-23T16:21:34Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.