# A Continuous Convolutional Trainable Filter for Modelling Unstructured Data

arXiv: https://arxiv.org/abs/2210.13416 · HTML: https://mlsanity.com/paper/2210.13416/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Recent Trends in Deep Learning Based Natural Language Processing](https://mlsanity.com/paper/1708.02709/) (2017)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [A Survey of Optimization Methods from a Machine Learning Perspective](https://mlsanity.com/paper/1906.06821/) (2019)
- [Towards a General Purpose CNN for Long Range Dependencies in ND](https://mlsanity.com/paper/2206.03398/) (2022)
- [The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations](https://mlsanity.com/paper/2108.06558/) (2021)
- [From Discrete to Continuous Convolution Layers](https://mlsanity.com/paper/2006.11120/) (2020)
- [Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method](https://mlsanity.com/paper/2203.00360/) (2022)

## Built on by (most cited first, 5 of 5)

- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)
- [QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression](https://mlsanity.com/paper/2211.05151/) (2022)
- [Enhancing Data-Assimilation in CFD using Graph Neural Networks](https://mlsanity.com/paper/2311.18027/) (2023)

## 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.