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

arXiv: https://arxiv.org/abs/2506.15845 · HTML: https://mlsanity.com/paper/2506.15845/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 18 Jun 2025.

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

- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [ClimAlign: Unsupervised statistical downscaling of climate variables via normalizing flows](https://mlsanity.com/paper/2008.04679/) (2020)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Algorithmic Hallucinations of Near-Surface Winds: Statistical Downscaling with Generative Adversarial Networks to Convection-Permitting Scales](https://mlsanity.com/paper/2302.08720/) (2023)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [A Survey on Error-Bounded Lossy Compression for Scientific Datasets](https://mlsanity.com/paper/2404.02840/) (2024)
- [COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence](https://mlsanity.com/paper/2205.01224/) (2022)
- [Capturing Climatic Variability: Using Deep Learning for Stochastic Downscaling](https://mlsanity.com/paper/2406.02587/) (2024)
- [Spatiotemporally adaptive compression for scientific dataset with feature preservation -- a case study on simulation data with extreme climate events analysis](https://mlsanity.com/paper/2401.03317/) (2024)
- [Compression and Conditional Emulation of Climate Model Output](https://mlsanity.com/paper/1605.07919/) (2016)
- [Implicit Neural Representations for Simultaneous Reduction and Continuous Reconstruction of Multi-Altitude Climate Data](https://mlsanity.com/paper/2409.17367/) (2024)

## Abstract (arXiv)

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.