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We propose methodologies to train highly accurate and efficient deep convolutional neural networks (CNNs) for image super resolution (SR). A cascade training approach to deep learning is proposed to improve the accuracy of the neural…
In this paper we show how the Smoothed Particle Hydrodynamics (SPH) equations for ideal magnetohydrodynamics (MHD) can be written in conservation form with the positivity of the dissipation guaranteed. We call the resulting algorithm…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…
Stacking-based deep neural network (S-DNN) is aggregated with pluralities of basic learning modules, one after another, to synthesize a deep neural network (DNN) alternative for pattern classification. Contrary to the DNNs trained end to…
The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters…
The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…
The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural…
Deep reinforcement learning (RL) is increasingly deployed in resource-constrained environments, yet the go-to function approximators - multilayer perceptrons (MLPs) - are often parameter-inefficient due to an imperfect inductive bias for…
For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings,…
In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and…
Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…
The event streams generated by dynamic vision sensors (DVS) are sparse and non-uniform in the spatial domain, while still dense and redundant in the temporal domain. Although spiking neural network (SNN), the event-driven neuromorphic…
Deep neural networks (DNNs) are becoming increasingly important components of software, and are considered the state-of-the-art solution for a number of problems, such as image recognition. However, DNNs are far from infallible, and…
There have been attempts to insert mathematical morphology (MM) operators into convolutional neural networks (CNN), and the most successful endeavor to date has been the morphological neural networks (MNN). Although MNN have performed…
Intra prediction is an important component of modern video codecs, which is able to efficiently squeeze out the spatial redundancy in video frames. With preceding pixels as the context, traditional intra prediction schemes generate linear…
Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…
The Moore-Penrose Pseudo-inverse (PInv) serves as the fundamental solution for linear systems. In this paper, we propose a natural generalization of PInv to the nonlinear regime in general and to neural networks in particular. We introduce…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer…
Over the past few years, Spiking Neural Networks (SNNs) have become popular as a possible pathway to enable low-power event-driven neuromorphic hardware. However, their application in machine learning have largely been limited to very…