A Continuous Convolutional Trainable Filter for Modelling Unstructured Data
arXiv:2210.13416 · doi:10.1007/s00466-023-02291-1
Abstract
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.
References in corpus (5)
- Deep Parametric Continuous Convolutional Neural Networks
- The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations
- A data driven reduced order model of fluid flow by Auto-Encoder and self-attention deep learning methods
- Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method
- Towards a General Purpose CNN for Long Range Dependencies in D