# Machine Learning Techniques for Data Reduction of CFD Applications

arXiv: https://arxiv.org/abs/2404.18063 · HTML: https://mlsanity.com/paper/2404.18063/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 28 Apr 2024.

## Builds on (most cited first, 8 of 8)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Image and Video Compression with Neural Networks: A Review](https://mlsanity.com/paper/1904.03567/) (2019)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression](https://mlsanity.com/paper/2211.05151/) (2022)
- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [SRN-SZ: Deep Leaning-Based Scientific Error-bounded Lossy Compression with Super-resolution Neural Networks](https://mlsanity.com/paper/2309.04037/) (2023)
- [A General Framework for Progressive Data Compression and Retrieval](https://mlsanity.com/paper/2308.11759/) (2023)

## Built on by (most cited first, 2 of 2)

- [Attention Based Machine Learning Methods for Data Reduction with Guaranteed Error Bounds](https://mlsanity.com/paper/2409.05357/) (2024)
- [Guaranteed Conditional Diffusion: 3D Block-based Models for Scientific Data Compression](https://mlsanity.com/paper/2502.12951/) (2025)

## Abstract (arXiv)

We present an approach called guaranteed block autoencoder that leverages Tensor Correlations (GBATC) for reducing the spatiotemporal data generated by computational fluid dynamics (CFD) and other scientific applications. It uses a multidimensional block of tensors (spanning in space and time) for both input and output, capturing the spatiotemporal and interspecies relationship within a tensor. The tensor consists of species that represent different elements in a CFD simulation. To guarantee the error bound of the reconstructed data, principal component analysis (PCA) is applied to the residual between the original and reconstructed data. This yields a basis matrix, which is then used to project the residual of each instance. The resulting coefficients are retained to enable accurate reconstruction. Experimental results demonstrate that our approach can deliver two orders of magnitude in reduction while still keeping the errors of primary data under scientifically acceptable bounds. Compared to reduction-based approaches based on SZ, our method achieves a substantially higher compression ratio for a given error bound or a better error for a given compression ratio.