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In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

Deep neural networks demonstrate to have a high performance on image classification tasks while being more difficult to train. Due to the complexity and vanishing gradient problem, it normally takes a lot of time and more computational…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Pan-sharpening is an important technique for remote sensing imaging systems to obtain high resolution multispectral images. Recently, deep learning has become the most popular tool for pan-sharpening. This paper develops a model-based deep…

Statistical shape modeling is an important tool to characterize variation in anatomical morphology. Typical shapes of interest are measured using 3D imaging and a subsequent pipeline of registration, segmentation, and some extraction of…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

In the design of tensegrity structures, traditional form-finding methods utilize kinematic and static approaches to identify geometric configurations that achieve equilibrium. However, these methods often fall short when applied to actual…

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Deep neural networks (DNN) have achieved unprecedented performance in computer-vision tasks almost ubiquitously in business, technology, and science. While substantial efforts are made to engineer highly accurate architectures and provide…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…

Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be…

Deep Convolutional Neural Networks (DCNN) have been proven to be effective for various computer vision problems. In this work, we demonstrate its effectiveness on a continuous object orientation estimation task, which requires prediction of…