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Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms.…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Recognizing text in the wild is a really challenging task because of complex backgrounds, various illuminations and diverse distortions, even with deep neural networks (convolutional neural networks and recurrent neural networks). In the…

Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational…

Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Alternating Direction Method of Multipliers (ADMM) has recently been proposed as a potential alternative optimizer to the Stochastic Gradient Descent(SGD) for deep learning problems. This is because ADMM can solve gradient vanishing and…

We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model…

On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Differential Equations (PDEs). It has been observed that DNNs are…

We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…

Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Large-scale deep learning models are increasingly constrained by their immense energy consumption, limiting their scalability and applicability for edge intelligence. In-memory computing (IMC) offers a promising solution by addressing the…