Related papers: Computing ground states of Bose-Einstein condensat…
Machine Learning methods are emerging as faster and efficient alternatives to numerical simulation techniques. The field of Scientific Computing has started adopting these data-driven approaches to faithfully model physical phenomena using…
Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative…
We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC). The main interest in such BEC comes from its important nature as macroscopic quantum…
The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel…
As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However,…
Distributed renewable generation, elastic loads, and purposeful manipulation of meter readings challenge the monitoring and control of today's power systems (PS). In this context, to maintain a comprehensive view of the system in real time,…
Batch Normalization (BN) has been proven to be quite effective at accelerating and improving the training of deep neural networks (DNNs). However, BN brings additional computation, consumes more memory and generally slows down the training…
Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has…
Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…
A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding…
We investigate the behavior of a Bose-Einstein Condensate (BEC) under the influence of a central barrier as the particle number trends towards the thermodynamic limit. In order to perform these studies, we present a novel method which is…
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…
Normalization is a pre-processing step that converts the data into a more usable representation. As part of the deep neural networks (DNNs), the batch normalization (BN) technique uses normalization to address the problem of internal…
Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…
The remarkable success of Deep Neural Networks(DNN) is driven by gradient-based optimization, yet this process is often undermined by its tendency to produce disordered weight structures, which harms feature clarity and degrades learning…
Conditioning analysis uncovers the landscape of an optimization objective by exploring the spectrum of its curvature matrix. This has been well explored theoretically for linear models. We extend this analysis to deep neural networks (DNNs)…
Batch Normalization (BN) techniques have been proposed to reduce the so-called Internal Covariate Shift (ICS) by attempting to keep the distributions of layer outputs unchanged. Experiments have shown their effectiveness on training deep…
We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations…
Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes…