mlsanityData to 7 Oct 2026

QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression

arXiv 2211.05151 ↗First posted 9 Nov 2022cs.LG cs.AI cs.CEcited by 6

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Abstract (arXiv)

We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. Moreover, the construction of our operator admits an efficient implementation which we detail and construct. As an experimental validation of our operator, we consider the task of compressing partial differential equation (PDE) simulation data from fixed meshes. We show that QuadConv can match the performance of standard discrete convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to a standard convolutional autoencoder (CAE). Further, we show that the QCAE can maintain this accuracy even on non-uniform data. In both cases, QuadConv also outperforms alternative unstructured convolution methods such as graph convolution.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 27 of its 51 references that are in the map. First posted on arXiv 9 Nov 2022.

Builds on

27 of 51 references.

References · 27

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15 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 1; 2026: 1.

6 papers.

  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2024Attention Based Machine Learning Methods for Data Reduction with Guaranteed Error Boundscited by 5
  3. 2023In Situ Framework for Coupling Simulation and Machine Learning with Application to CFDcited by 2
  4. 2024Machine Learning Techniques for Data Reduction of CFD Applicationscited by 2
  5. 2026GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domainscited by 1
  6. 2025In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularizationcited by 0