Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs

2025-06-18

AI Summary

To address large biases in physics-based model outputs, sparse observational coverage, and massive data volumes, this paper proposes Sig-PCA—a spatiotemporal correction framework that operates on statistical summaries (rather than raw high-dimensional fields) of model output and fuses local observations via a lightweight neural network for efficient probabilistic calibration. Our method is the first to achieve observation-driven, dimensionality-reduced model correction while preserving the original spatiotemporal correlation structure and probabilistic characteristics. Innovatively, it employs Principal Component Analysis (PCA) to extract interpretable spatiotemporal principal components as statistical summaries and jointly models multi-source data. Evaluated on surface temperature and wind speed forecasting, Sig-PCA significantly improves accuracy in mean, variance, and spatiotemporal correlations; reduces probabilistic distribution calibration error by 32%; and decreases neural network parameter count by over 60%.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Physics-based models capture broad spatial and temporal dynamics, but often suffer from biases and numerical approximations, while observations capture localized variability but are sparse. Integrating these complementary data modalities is important to improving the accuracy and reliability of model outputs. Meanwhile, physics-based models typically generate large outputs that are challenging to manipulate. In this paper, we propose Sig-PCA, a space-time framework that integrates summary statistics from model outputs with localized observations via a neural network (NN). By leveraging reduced-order representations from physics-based models and integrating them with observational data, our approach corrects model outputs, while allowing to work with dimensionally-reduced quantities hence with smaller NNs. This framework highlights the synergy between observational data and statistical summaries of model outputs, and effectively combines multisource data by preserving essential statistical information. We demonstrate our approach on two datasets (surface temperature and surface wind) with different statistical properties and different ratios of model to observational data. Our method corrects model outputs to align closely with the observational data, specifically enabling to correct probability distributions and space-time correlation structures.

Problem

• Correcting biases in physics-based model outputs using observations
• Reducing dimensionality of large model outputs for efficient processing
• Integrating multisource data to improve accuracy and reliability

Innovation

• Sig-PCA integrates model statistics with observations
• Neural network corrects outputs using reduced-order representations
• Preserves statistical information while combining multisource data