mlsanityData to 7 Oct 2026

A Continuous Convolutional Trainable Filter for Modelling Unstructured Data

arXiv 2210.13416 ↗First posted 24 Oct 2022cs.LG cs.NA math.NAcited by 5

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Abstract (arXiv)

Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 23 of its 53 references that are in the map. First posted on arXiv 24 Oct 2022.

Builds on

23 of 53 references.

References · 23

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  5. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  6. 2014Going Deeper with Convolutionscited by 4,231
  7. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  8. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  9. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  10. 2016An overview of gradient descent optimization algorithmscited by 1,021
  11. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  12. 2020A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospectscited by 396
11 more
  1. 2017Recent Trends in Deep Learning Based Natural Language Processingcited by 262
  2. 2017EMNIST: an extension of MNIST to handwritten letterscited by 212
  3. 2016A guide to convolution arithmetic for deep learningcited by 182
  4. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  5. 2021Dive into Deep Learningcited by 111
  6. 2016Learning shape correspondence with anisotropic convolutional neural networkscited by 95
  7. 2019A Survey of Optimization Methods from a Machine Learning Perspectivecited by 90
  8. 2022Towards a General Purpose CNN for Long Range Dependencies in NDcited by 16
  9. 2021The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equationscited by 14
  10. 2020From Discrete to Continuous Convolution Layerscited by 7
  11. 2022Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation methodcited by 7

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Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 0; 2025: 1.

5 papers.

  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2025Machine learning for modelling unstructured grid data in computational physics: a reviewcited by 12
  3. 2023Generative Adversarial Reduced Order Modellingcited by 7
  4. 2022QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compressioncited by 6
  5. 2023Enhancing Data-Assimilation in CFD using Graph Neural Networkscited by 0