Soliton, breather, and rogue wave solutions for solving the nonlinear Schrodinger equation using a deep learning method with physical constraints

The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schrodinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schrodinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.

A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions

Recent years have witnessed growing interests in solving partial differential equations by deep neural networks,especially in the high-dimensional case.Unlike classical numerical methods,such as finite difference method and finite element method,the enforcement of boundary conditions in deep neural networks is highly nontrivial.One general strategy is to use the penalty method.In the work,we conduct a comparison study for elliptic problems with four different boundary conditions,i.e.,Dirichlet,Neumann,Robin,and periodic boundary conditions,using two representative methods:deep Galerkin method and deep Ritz method.In the former,the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter.Therefore,it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions.However,by a number of examples,we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.Besides,in some cases,when the boundary condition can be implemented in an exact manner,we find that such a strategy not only provides a better approximate solution but also facilitates the training process.

Predicting the 25th solar cycle using deep learning methods based on sunspot area data

It is a significant task to predict the solar activity for space weather and solar physics. All kinds of approaches have been used to forecast solar activities, and they have been applied to many areas such as the solar dynamo of simulation and space mission planning. In this paper, we employ the long-shortterm memory(LSTM) and neural network autoregression(NNAR) deep learning methods to predict the upcoming 25 th solar cycle using the sunspot area(SSA) data during the period of May 1874 to December2020. Our results show that the 25 th solar cycle will be 55% stronger than Solar Cycle 24 with a maximum sunspot area of 3115±401 and the cycle reaching its peak in October 2022 by using the LSTM method. It also shows that deep learning algorithms perform better than the other commonly used methods and have high application value.

RESEARCH ON THE EVALUATION METHOD OF FRICTION AND LUBRICATION IN DEEP DRAWING

The deformation characteristic of bland in deep drawing is discussed. It is pointed out that the friction and lubrication conditions in for drawing are different from that in mechanical motion or machine work or other plastic process. The common test methods in laboratories are analyzed. It shows that though all those test methods can test the friction coefficient, the probe test method is most suitable for the research of friction and lubrication and the process in deep drawing, for this method is identical with the actual work condition either from the test principle or deformation status of the blank. Last the successful application in the deep drawing simulator newly developed the the probe method are intro- duced in detail.

Dynamic Analysis of Deep-Ocean Mining Pipe System by Discrete Element Method

The dynamic analysis of a pipe system is one of the most crucial problems for the entire mining system. A discrete element method （DEM） is proposed for the analysis of a deep-ocean mining pipe system, including the lift pipe, pump, buffer and flexible hose. By the discrete element method, the pipe is divided into some rigid elements that are linked by flexible connectors. First, two examples representing static analysis and dynamic analysis respectively are given to show that the DEM model is feasible. Then the three-dimensional DEM model is used for dynamic analysis of the mining pipe system. The dynamic motions of the entire mining pipe system under different work conditions are discussed. Some suggestions are made for the actual operation of deep-ocean mining systems.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

Least Squares Method from the View Point of Deep Learning

The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares. In this paper we reconsider the least squares method from the view point of Deep Learning and we carry out the computation thoroughly for the gradient descent sequence in a very simple setting. Depending on the values of the learning rate, an essential parameter of Deep Learning, the least squares methods of Statistics and Deep Learning reveal an interesting difference.

Least Squares Method from the View Point of Deep Learning II: Generalization

The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares method, in which a parameter called learning rate plays an important role. It is in general very hard to determine its value. In this paper we generalize the preceding paper [K. Fujii: Least squares method from the view point of Deep Learning: Advances in Pure Mathematics, 8, 485-493, 2018] and give an admissible value of the learning rate, which is easily obtained.

Optimization of control of network with inverse method of deep foundation

Following the theory of CPM/PERT, and using the inverse method of deep foundation in tall buildings, how to control a project with network and how to optimize this network by computer are discussed, and by comparing and analyzing the working schemes and taking into account time and economy, "the means of the lowest cost accelerating(MLCA)" is used to make optimal computation for critical paths and take into consideration the influence of cold weather on construction and foundation treatment etc, so that the best work can be done at the lowest cost.

A method for detecting the breaking of wind-generated waves in deep water

The breaking of wind-generated waves is an important phenomenon in the ocean, having close relation to many aspects of the ocean, such as air-sea interaction, ocean wave dynamics, oceanic remote sensing and ocean engineering. The first problem encountered in both its theoretical study and practical measurement is how to detect the breaking of waves.

Cognitive Control and Brain Network Dynamics during Word Generation Tasks Predicted Using a Novel Event-Related Deep Brain Activity Method

There is a growing interest in the diagnosis and treatment of patients with dementia and cognitive impairment at an early stage. Recent imaging studies have explored neural mechanisms underlying cognitive dysfunction based on brain network architecture and functioning. The dorsal anterior cingulate cortex (dACC) is thought to regulate large-scale intrinsic brain networks, and plays a primary role in cognitive processing with the anterior insular cortex (aIC), thus providing salience functions. Although neural mechanisms have been elucidated at the connectivity level by imaging studies, their understanding at the activity level still remains unclear because of limited time-based resolution of conventional imaging techniques. In this study, we investigated temporal activity of the dACC during word (verb) generation tasks based on our newly developed event-related deep brain activity (ER-DBA) method using occipital electroencephalogram (EEG) alpha-2 powers with a time resolution of a few hundred milliseconds. The dACC exhibited dip-like temporal waveforms indicating deactivation in an initial stage of each trial when appropriate verbs were successfully generated. By contrast, monotonous increase was observed for incorrect responses and a decrease was detected for no responses. The dip depth was correlated with the percentage of success. Additionally, the dip depth linearly increased with increasing slow component of the DBA index at rest across all subjects. These findings suggest that dACC deactivation is essential for cognitive processing, whereas its activation is required for goal-oriented behavioral outputs, such as cued speech. Such dACC functioning, represented by the dip depth, is supported by the activity of the upper brainstem region including monoaminergic neural systems.

Bearing Capacity Assessment of Collapsible Soils Improved by Deep Soil Mixing Using Finite Element Method

Problematic soils usually cause considerable problems to engineering projects. As an example, soil structure collapse caused by moisture increment or rising underground water level results in huge settlements. This type of problematic soil, named collapsible soil, can cause dramatic problems and should be amended where exists. Today, the use of different techniques for soil reinforcement and soil improvement is widely used to treat soil properties. One of these methods is Deep Soil Mixing (DSM) method. This method becomes more important in the cases of studying and examining collapsible soils. In this research, the settlement of amended collapsible soils, applying deep soil mixing method, is examined. The experiments show that soil amendment using this method, well prevents the settlement of collapsible soils giving rise to bearing capacity.

Application of the “Three Threes” Method in Clinical Teaching of Internal Jugular Vein Puncture

Objective: To clarify the role of the “Three Threes” method in clinical teaching of internal jugular vein puncture and explore improvements in teaching methods. Methods: A doctor was assigned to the induction room of the Second Affiliated Hospital of Naval Medical University (Shanghai Changzheng Hospital) for two months. The time required for catheterization, the first puncture success rate, and occurrence of puncture-related complications were compared before and after learning the “Three Threes” method. Results: Using the “Three Threes” method reduced the catheterization time by 43%, increased the first puncture success rate by 17%, and led to fewer puncture-related complications. Conclusion: The application of the “Three Threes” method not only improves the success rate of internal jugular vein puncture but also reduces complications, making it easier for students to master the technique.

Stoichiometry and Stability Constant Values for Copper (II) Chelates with Ethylene Diamine in Deep Eutectic Solvents (DES) (Ethaline) Solutions

In this study we used the deep eutectic solvents (ionic liquids) to investigate the reaction between copper (II) with ethylene diamine (en). Two of the existing methods for analyzing spectrophotometric measurements have been applied for establishing, the stoichiometry and whenever possible, the stability constants of the chelates formed. The method of continuous variations was necessary to determine first whether, the metal ion and the ligand ethylene diamine form one or more than one chelate, when more than one chelate formed, the results obtained depend on the wavelength and for meaningful conclusions the wavelengths were carefully selected. The empirical formulae of the chelates were further substantiated by the molar ratio method. The effect of time and temperature on the formation and stability of these chelates in solution is also studied. The stability constants, K1 and K2 for the copper (II) chelates were calculated, though reliable, and are comparable to literature values.

基于DeepLabV3+模型改进的图像分割方法研究

近年来,计算机视觉快速发展,其中图像分割在计算机视觉中也举足轻重,在城市现代化建设,智能驾驶,地理勘测等方面都得到了充分应用。但是,大多数分割方法只关注图像特征的纵向深层特征与浅层特征的简单融合,而忽略了同一层图像特征的横向远程关系。针对此问题,基于DeepLabV3+框架,加入Swin-Transformer block,利用其自注意力机制特点,进行网络特征提取,以提高图像分割的全局和细节优化。其次,改进DeepLabV3+中上采样方法,利用CARAFE上采样模块取代简单的双线性插值法。实验表明,改进后的模型相较于基线模型MIoU提升2%,ACC提升1%。

虚拟震源地震探测方法及其应用

SsPmp震相是远震直达S波在地表激发的下行P波在Moho面反射的震相,具有信号能量大、信噪比高、不易受近地表沉积层和地壳小尺度结构扰动的影响等优势.虚拟地震测深方法(VDSS)是近年来发展的利用SsPmp震相与直达Ss波震相的到时差来研究地壳厚度(或Moho面深度)的探测方法.本文介绍了VDSS方法的原理、优势及其在实际应用中的表现.研究表明,VDSS方法在提高探测精度、降低成本、环境影响等方面具有显著优势,且成功应用于克拉通、造山带和沉积盆地、峨眉山大火成岩省等不同地质环境中,在探测地壳结构中展现出巨大潜力和应用价值.但是VDSS方法的准确度高度依赖于地震数据的质量,尤其是远震S波的清晰度和震中距的范围,使得该方法在复杂地质结构区域的应用受到较大限制.未来,VDSS与传统接收函数方法、地震层析成像、重力测量等多类地球物理方法的结合,有望为地壳结构探测提供更全面的约束.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Deep postbuckling and nonlinear bending behaviors of nanobeams with nonlocal and strain gradient effects

In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.

Deep Web数据抽取的分析与研究

从各web站点抽取数据是Deep Web数据集成研究中的重要内容.重点分析数据抽取策略,使用HttpClient工具获取Deep Web页面及其各个分页,并提出了基于样式的定位方法处理被查询页面.最后,为验证提出的数据抽取方案的可行性,实现了一个Deep Web实际应用系统,运行效果表明方案有效可行,较好地解决了数据抽取准确性的问题.

深水钢桁梁无承台特大桥无应力状态法合龙应用研究

深水区域钢桁梁特大桥无承台桩基施工需要特别考虑施工工艺及其受力体系控制。依托四川汉源兰家湾特大桥工程,基于无应力状态方法分析计算钢桁梁特大桥的无桩基承台施工技术以及合龙施工的若干力学研究。结果表明,通过搭建深水区域无承台的特大桥桩墩结合施工,在其上进行钢桁梁安装拼接的无应力状态法合龙施工可取得良好受力整体性效果。所述方法可解决在较深水流条件下的特大桥桩基施工与整体受力控制难题,可为类似工程提供技术参考和借鉴。