Related papers: Deep Neural Networks Motivated by Partial Differen…
Deep convolutional neural network (DCNN) based supervised learning is a widely practiced approach for large-scale image classification. However, retraining these large networks to accommodate new, previously unseen data demands high…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Traditional architectures for solving computer vision problems and the degree of success they enjoyed have been heavily reliant on hand-crafted features. However, of late, deep learning techniques have offered a compelling alternative --…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in…
Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different…
This paper presents a new variational inference framework for image restoration and a convolutional neural network (CNN) structure that can solve the restoration problems described by the proposed framework. Earlier CNN-based image…
Providing fast and accurate solutions to partial differential equations is a problem of continuous interest to the fields of applied mathematics and physics. With the recent advances in machine learning, the adoption learning techniques in…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Deep Convolutional Neural Networks (CNNs) for image classification successively alternate convolutions and downsampling operations, such as pooling layers or strided convolutions, resulting in lower resolution features the deeper the…
In the last decade Convolutional Neural Networks (CNNs) have defined the state of the art for many low level image processing and restoration tasks such as denoising, demosaicking, upscaling, or inpainting. However, on-device mobile…
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…
Deep-neural-network-based image reconstruction has demonstrated promising performance in medical imaging for under-sampled and low-dose scenarios. However, it requires large amount of memory and extensive time for the training. It is…
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…
This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance…