Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy's law

A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equa- tions with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be sta- bly numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy＇s flow problem, the exact analytical solution for the case of Darcy＇s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclu- sion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equa- tions; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pres- sure gradient increasing for the one-dimensional problem.

On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term

The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.

CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT

In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.

Exact boundary behavior of large solutions to semilinear elliptic equations with a nonlinear gradient term

This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.

GLOBAL EXISTENCE AND EXTINCTION FOR A DEGENERATE NONLINEAR DIFFUSION PROBLEM WITH NONLINEAR GRADIENT TERM AND ABSORPTION

Existence and extinction in finite time of global weak solutions for the problem （P） are proved.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

Novel image restoration model coupling gradient fidelity term based on adaptive total variation

A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretically, and a simple scheme to demonstrate its validity was adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm was used to solve partial differential equations. Both the international standard test image on Lena and HR image of CBERS-02B of Dalian city were used to verify the performance of the model. Experimental results illustrate that the new model not only preserved the edge and important details but also alleviated the staircase effect effectively.

CONVERGENCE OF ONLINE GRADIENT METHOD WITH A PENALTY TERM FOR FEEDFORWARD NEURAL NETWORKS WITH STOCHASTIC INPUTS

Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.

Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations

In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.

Online Gradient Methods with a Punishing Term for Neural Networks

Online gradient methods are widely used for training the weight of neural networks and for other engineering computations. In certain cases, the resulting weight may become very large, causing difficulties in the implementation of the network by electronic circuits. In this paper we introduce a punishing term into the error function of the training procedure to prevent this situation. The corresponding convergence of the iterative training procedure and the boundedness of the weight sequence are proved. A supporting numerical example is also provided.

Effects of Long-Term Fertilization on Different Nitrogen Forms in Paddy along Soil Depth Gradient

The combined application of organic fertilizer and chemical fertilizer is an effective measure to increase nutrient content of soil plough layer, which must have a profound impact on the deep soil nutrients, especially the contents of nitrogen forms. The purpose of this study was to explore the characteristics of soil nitrogen forms in plough layer and along depth gradient in different fertilization treatments, so as to evaluate the soil quality in spatial dimension, further providing a theoretical basis for scientific fertilization and improvement of paddy soil fertility. Here, a 34-year field experiment was conducted with three treatments: without any fertilizer (CK), pure chemical fertilizer (NPK) and chemical fertilizer combined with organic fertilizer (NPKM). We analyzed the content of nitrogen forms in 0 - 100 cm soil depth and their ratios to total nitrogen (TN), and discussed the correlation between nitrogen forms contents and pH, CEC. Results showed that, compared with CK, both NPK and NPKM significantly increased the contents of nitrogen forms in topsoil (soil layer of 0 - 20 cm), especially nitrate nitrogen (NO3--N) content increased by 70% (NPK) and 111% (NPKM), respectively. Although the contents of different nitrogen forms decreased gradually along soil depth gradient, NPKS slowed down the decline rate of TN and alkali-hydrolysable nitrogen (AN) in 0 - 60 cm soil layer, compared to CK. Compared to NPK, NPKM significantly increased the NO3--N/TN ratio in 0 - 20 cm soil layer, but also decreased the content of -N in 20 - 40 cm, which was beneficial to reduce the risk of nitrogen leaching caused by nitrate leaching into deep layer. The increase of soil pH in NPKM treatment obviously alleviated the problem of soil acidification caused by long-term application of chemical fertilizer. Correlation analysis showed that there was a significant positive correlation between soil nitrogen forms and cation exchange capacity (CEC), but no significant correlation with soil pH. In conclusion, NPKM ensured the nutrients of soil plough layer (0 - 20 cm), also reduced the risk of nitrogen infiltration and nitrogen loss, thus ensuring the fertility of soil profile.

基于BiLSTM-XGBoost混合模型的储层岩性识别

储层岩性分类是地质研究基础,基于数据驱动的机器学习模型虽然能较好地识别储层岩性,但由于测井数据是特殊的序列数据,模型很难有效提取数据的空间相关性,造成模型对储层识别仍存在不足.针对此问题,本文结合双向长短期循环神经网络(bidirectional long short-term memory,BiLSTM)和极端梯度提升决策树(extreme gradient boosting decision tree,XGBoost),提出双向记忆极端梯度提升(BiLSTM-XGBoost,BiXGB)模型预测储层岩性.该模型在传统XGBoost基础上融入了BiLSTM,大大增强了模型对测井数据的特征提取能力.BiXGB模型使用BiLSTM对测井数据进行特征提取,将提取到的特征传递给XGBoost分类模型进行训练和预测.将BiXGB模型应用于储层岩性数据集时,模型预测的总体精度达到了91%.为了进一步验证模型的准确性和稳定性,将模型应用于UCI公开的Occupancy序列数据集,结果显示模型的预测总体精度也高达93%.相较于其他机器学习模型,BiXGB模型能准确地对序列数据进行分类,提高了储层岩性的识别精度,满足了油气勘探的实际需要,为储层岩性识别提供了新的方法.

基于考虑误差修正的非线性自适应权重组合模型的光伏发电功率预测

为了提高光伏电站光伏发电功率预测精度,解决极限梯度提升模型、长短期记忆模型2种传统单一模型及传统组合模型极限梯度提升-长短期记忆模型的光伏发电功率预测结果滞后、预测效果易突变、预测误差较大、线性拟合性较差等不足,基于极限梯度提升算法、长短期记忆算法和线性自适应权重,提出一种考虑误差修正的非线性自适应权重极限梯度提升-长短期记忆模型进行光伏发电功率预测;分别使用极限梯度提升算法和长短期记忆算法训练得到2种单一模型,将2种单一模型的初步预测值和真实值组成新的训练数据集,利用神经网络算法训练所提出的模型,对2种单一模型的初步预测值分配自适应权重系数,并根据训练时所提出模型的预测值大小分段统计预测误差的分布,预测时根据所提出模型的预测值在预测结果的基础上累加误差均值从而进行误差修正,进一步提高所提出模型的预测精度;利用Python语言分别对所提出的模型、传统组合模型和2种传统单一模型在晴天、阴天和雨天的光伏发电功率预测性能进行仿真。结果表明:与极限梯度提升-长短期记忆模型、极限梯度提升模型、长短期记忆模型相比,所提出模型的均方根误差分别减小28.57%、 39.39%、 49.79%,平均绝对误差分别减小44.25%、 53.33%、 64.8%,决定系数分别增大1.43%、 2.38%、 3.34%,所提出的模型更有效地减小了传统单一模型的光伏发电功率预测误差,优化了传统组合模型的权重系数;3种天气条件下所提出模型的光伏发电功率预测误差相对最小且稳健性最强,验证了所提出模型的有效性。

两阶段非负矩阵分解算法及其在光谱解混中的应用

非负矩阵分解问题(nonnegative matrix factorization,NMF)模型已成功应用至高光谱遥感影像处理中的光谱解混工作,由于NMF优化模型具有多个局部极小点,使得分解结果不稳定。设计初始化方法或者选择带正则项的问题模型是提高分解精度的两种常用方法。本文提出了两阶段的NMF算法,实现了初始点选取和正则项设计的结合。第一阶段借助k-均值获得k个聚类中心,给出迭代的初始点;利用第一阶段的初始矩阵U^(0),定义了针对端元矩阵的正则项‖U-U^(0)‖_(F)^(2),第二阶段采用基于交替非负最小二乘框架的投影梯度算法,求解新的正则化NMF问题。正则项中的端元初始矩阵U^(0)除了采用k-均值获得k个聚类中心,也可采用真实地物光谱,它的引入提高了算法的灵活度。数值结果表明新算法更加稳定,且分解的精确性有效提高。

1961—2020年长江下游地区夏季降水趋势分析

近几十年来长江下游地区夏季(6—8月)降水量呈现出显著上升的变化趋势,利用1961—2020年夏季台站降水资料,通过降水项分解法,定量分析了该降水趋势的可能影响因素。结果表明:1)长江下游地区夏季降水的上升趋势主要是由日降水量显著增加造成,而日降水量显著增加主要与整层水汽垂直梯度增大和垂直上升速度增强所导致的降水增加有关;2)长江下游地区对流层低层大气温度因地面升温的加热作用而显著上升,高层大气温度受亚太振荡相位正转负的影响而下降,使得高、低层大气的温差变大,低层大气比湿升高、高层大气比湿降低,导致整层水汽垂直梯度增加,为局地降水的增强提供了充沛的水汽条件;低层大气异常辐合加之显著增长的不稳定能量为垂直上升运动的增强和对流性降水的增加提供了有利的动力和热力条件,从而造成了长江下游地区夏季降水的显著上升趋势。

基于频率分解的机器学习模型预测效果比较

文章引入一种小波变换与机器学习的组合预测方法,通过小波变换提取单变量时间序列的主要特征,并应用不同的机器学习模型进行预测分析。构建不同类型的机器学习模型对上证指数、恒生指数、纳斯达克指数和日经225指数进行预测,结果表明:在不增加任何被解释变量的情况下,经过小波变换的数据特征能较好地预测指数收益率;通过比较线性模型、机器学习模型和深度学习模型发现,线性模型在捕获小波变换特征方面表现最好;有效的数据降维方法是提高非线性模型样本外预测精度的重要手段,并且可以减少模型训练的时间;小波变换和贝叶斯混合模型的预测精度高于传统的ARMA模型。

基于长短期记忆网络和梯度提升的高血压患者RR间期时间序列预测方法

目的 对高血压患者的RR间期进行预测,帮助临床医生对患者心脏状况进行分析和预警。方法 以8位患者数据为样本,通过长短期记忆网络(LSTM)和梯度提升树(XGBoost)分别对患者的RR间期进行预测,将2个模型的预测结果通过方差倒数法进行组合,克服单一模型预测的劣势。结果 提出的组合模型相较于单一模型在8位患者RR间期的预测上具有不同程度的改善效果。结论 LSTM-XGBoost模型为高血压患者RR间期预测提供了方法,具有一定的临床价值。

SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.

大规模电力工程数据价值深度挖掘算法设计研究

针对传统电力工程数据处理方法中存在的不可追溯且不易统一管理等问题,文中基于数据挖掘的思想提出了一种电力工程数据价值分析预测模型。该模型采用Boosting算法将多个预测树结构组合形成极端梯度提升树模型,从而实现对非线性数据的深入分析,且经过多次迭代后,可以使训练准确度与学习效果得到显著提升。通过采用改进的双向长短时记忆网络,增强了模型处理时序性数据的能力。同时还使用误差倒数法将两个算法模型相结合,使其具有更高的预测精度。在实验测试中,所提算法的预测结果更贴近实际值,且其MAPE及RMSE测试指标分别为0.201%和0.039%,在所有对比算法中均为最优,可以对电力工程数据价值进行准确的分析和预测。

用梯度提升决策树实现电力负荷非线性影响因素分析

为了避免由因素冗余导致的预测精度下降,对比分析了6种集成机器学习模型的性能,发现梯度提升决策树回归模型性能最好。利用梯度提升决策树进行特征重要性排序,选出显著影响因素;然后通过计算偏依赖量来评估各影响因素与最大负荷之间的非线性关系;最后,运用长短期记忆预测模型对各个因素的组合进行验证。结果表明,利用梯度提升决策树可以有效捕捉最大负荷与各因素之间的非线性关系,且经过因素选择和考虑温度累积效应后,负荷预测准确度得到显著提高。