Related papers: Convolutional-neural-operator-based transfer learn…
This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
Convolutional neural networks (CNNs) have constantly achieved better performance over years by introducing more complex topology, and enlarging the capacity towards deeper and wider CNNs. This makes the manual design of CNNs extremely…
A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…
Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…
In this paper we propose cross-modal convolutional neural networks (X-CNNs), a novel biologically inspired type of CNN architectures, treating gradient descent-specialised CNNs as individual units of processing in a larger-scale network…
When optimizing convolutional neural networks (CNN) for a specific image-based task, specialists commonly overshoot the number of convolutional layers in their designs. By implication, these CNNs are unnecessarily resource intensive to…
This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…
Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, the image convolution has…
Convolutional Neural Networks (CNNs), architectures consisting of convolutional layers, have been the standard choice in vision tasks. Recent studies have shown that Vision Transformers (VTs), architectures based on self-attention modules,…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…
Traditional Convolutional Neural Networks have been successful in capturing local, position-invariant features in text, but their capacity to model complex transformation within language can be further explored. In this work, we explore a…
Large machine learning models based on Convolutional Neural Networks (CNNs) with rapidly increasing number of parameters, trained with massive amounts of data, are being deployed in a wide array of computer vision tasks from self-driving…
Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In…
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…
In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practitioners with new powerful data-driven techniques such as…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…
Recently, outstanding identification rates in image classification tasks were achieved by convolutional neural networks (CNNs). to use such skills, selective CNNs trained on a dataset of well-known images of metal surface defects captured…