Related papers: Computing ground states of Bose-Einstein condensat…

Various normalization layers have been proposed to help the training of neural networks. Group Normalization (GN) is one of the effective and attractive studies that achieved significant performances in the visual recognition task. Despite…

Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…

Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…

A multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value…

Normalization layers are critical components of modern AI systems, such as ChatGPT, Gemini, DeepSeek, etc. Empirically, they are known to stabilize training dynamics and improve generalization ability. However, the underlying theoretical…

We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasi-classical regimes of Landau damping. We use a generalized wave-kinetic description of BECs…

Evolutional deep neural networks (EDNN) solve partial differential equations (PDEs) by marching the network representation of the solution fields, using the governing equations. Use of a single network to solve coupled PDEs on large domains…

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation (BEC), which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined…

Batch Normalization (BN) is a popular technique for training Deep Neural Networks (DNNs). BN uses scaling and shifting to normalize activations of mini-batches to accelerate convergence and improve generalization. The recently proposed…

Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an estimate for the generalization error of learning Lipschitz…

In this paper, we investigate lossy compression of deep neural networks (DNNs) by weight quantization and lossless source coding for memory-efficient deployment. Whereas the previous work addressed non-universal scalar quantization and…

Convolutional neural networks (CNNs) have achieved great successes in many computer vision problems. Unlike existing works that designed CNN architectures to improve performance on a single task of a single domain and not generalizable, we…

This work considers a challenging Deep Neural Network(DNN) quantization task that seeks to train quantized DNNs without involving any full-precision operations. Most previous quantization approaches are not applicable to this task since…

Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann electrostatics. These problems are characterized by sharp…

Deep learning (DL) has been applied extensively in many computational imaging problems, often leading to superior performance over traditional iterative approaches. However, two important questions remain largely unanswered: first, how well…

Normalization techniques are important in different advanced neural networks and different tasks. This work investigates a novel dynamic learning-to-normalize (L2N) problem by proposing Exemplar Normalization (EN), which is able to learn…

In image enhancement tasks, such as low-light and underwater image enhancement, a degraded image can correspond to multiple plausible target images due to dynamic photography conditions. This naturally results in a one-to-many mapping…

Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full precision counterparts. To maintain the same performance level especially at low bit-widths,…

We introduce a deep neural network (DNN) framework called the \textbf{r}eal-space \textbf{a}tomic \textbf{d}ecomposition \textbf{net}work (\textsc{radnet}), which is capable of making accurate polarization and static dielectric function…

In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential…