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Traditional methods for motion estimation estimate the motion field F between a pair of images as the one that minimizes a predesigned cost function. In this paper, we propose a direct method and train a Convolutional Neural Network (CNN)…

To reduce memory footprint and run-time latency, techniques such as neural network pruning and binarization have been explored separately. However, it is unclear how to combine the best of the two worlds to get extremely small and efficient…

In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…

In this paper, we provide a novel Model-free approach based on Deep Neural Network (DNN) to accomplish point prediction and prediction interval under a general regression setting. Usually, people rely on parametric or non-parametric models…

Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i)…

FPN is a common component used in object detectors, it supplements multi-scale information by adjacent level features interpolation and summation. However, due to the existence of nonlinear operations and the convolutional layers with…

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…

We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…

Physics-Informed Neural Network (PINN) has become a commonly used machine learning approach to solve partial differential equations (PDE). But, facing high-dimensional secondorder PDE problems, PINN will suffer from severe scalability…

Physics-informed neural networks (PiNNs) recently emerged as a powerful solver for a large class of partial differential equations under various initial and boundary conditions. In this paper, we propose trapz-PiNNs, physics-informed neural…

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…

By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…

An Undirected Weighted Network (UWN) is commonly found in big data-related applications. Note that such a network's information connected with its nodes, and edges can be expressed as a Symmetric, High-Dimensional and Incomplete (SHDI)…

It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit biases underlying the training process of DNNs, such as the…

We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates…

The advent of foundation models in AI has significantly advanced general-purpose learning, enabling remarkable capabilities in zero-shot inference and in-context learning. However, training such models on physics data, including solutions…

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…