在本文中，提出了一种在高阶导数空间中的本地图案描述符用于面部识别。所提出的局部定向梯度模式（LDGP）是通过在四个不同的方向上编码参考像素的高阶导数之间的关系来计算的1D局部微图案。所提出的描述符识别来自四个不同方向的引用像素的高阶导数之间的关系，以计算对应于本地特征的微图案。所提出的描述符显着降低了微图案的长度，从而降低了提取时间和匹配时间，同时保持识别率。在基准数据库中进行的广泛实验的结果，延伸耶鲁B和CMU-PIE的基准数据库，表明所提出的描述符显着降低了提取以及匹配时间，同时识别率几乎类似于现有技术的现有技术。

特征描述是专家系统和机器学习中最常见的区域之一。有效编码图像是准确匹配的必要要求。这些编码方案在识别和检索系统中发挥着重要作用。面部识别系统应该有效地在系统内在和外在变化下准确地识别个体。这些系统中使用的模板或描述符编码图像的本地附近的像素的空间关系。使用这些手工制作描述符编码的功能应该是稳健的抵抗诸如;照明，背景，姿势和表达。在本文中，提出了一种新型手工制作的级联非对称局部图案（CALP），用于检索和识别面部图像。所提出的描述符在水平和垂直方向上唯一地对相邻像素之间的关系进行唯一编码关系。所提出的编码方案具有最佳特征长度，并且在面部图像中的环境和生理变化下的准确性显着提高。艺术手工制作描述符的状态即;将LBP，LDGP，CSLBP，SLBP和CSLTP与最具挑战性数据集上的所提出的描述符进行比较。 Caltech-Face，LFW和Casia-Face-V5。结果分析表明，在表情，背景，姿势和照明的不受控制的变化下，所提出的描述符优于现有技术。

本文提出了一种新颖的手工制作的本地四重模式（LQPAT），用于面部图像识别和检索。大多数现有的手工制作描述符在本地邻域中仅编码有限数量的像素。在不受约束的环境下，这些描述符的性能往往会急剧降级。增加本地邻居的主要问题是，它还增加了描述符的特征长度。所提出的描述符尝试通过定义具有最佳特征长度的有效编码结构来克服这些问题。所提出的描述符在二次空间中的邻居中的关系编码。从本地关系计算两个微图案以形成描述符。所提出的描述符的检索和识别精度已经与替补标记数据库上的艺术手工制作描述符的状态进行了比较; Caltech-Face，LFW，Color-Feret和Casia-Face-V5。结果分析表明，所提出的描述符在姿势，照明，背景和表达式的不受控制的变化下执行良好。

面部特征被定义为面部图像的像素中存在的局部关系。手工制作的描述符确定内核定义的本地邻域中的像素的关系。内核是一种二维矩阵，它在面部图像上移动。内核捕获的具有有限数量的像素的独特信息实现了在受约束环境下拍摄的面部图像上的令人满意的识别和检索精度（光，姿势，表达式和背景的受控变化）。为了在不受约束的环境下实现类似的准确性，必须增加本地社区，以便编码更多像素。增加本地邻域也增加了描述符的特征长度。在本文中，我们提出了一种手工制作的描述符，即中心对称四重奏模式（CSQP），其在结构上对称，并在四重空间中对面部不对称进行编码。所提出的描述符有效地编码具有最佳二进制位数的较大邻域。已经示出了使用平均熵，计算与所提出的描述符编码的特征图像，CSQP与艺术描述符的状态相比捕获更有意义的信息。将所提出的描述符的检索和识别精度与在台式标记数据库上的艺术手工描述符（CSLBP，CSLTP，LDP，LBP，SLBP和LDGP）的状态进行了比较; LFW，Color-Feret和Casia-Face-V5。结果分析表明，所提出的描述符在受控和姿势，照明，背景和表达中的不受控制的变化下执行良好。

在面部识别中使用的本地描述符是稳健的，因为这些描述符在不同的姿势，照明和照明条件下表现良好。这些描述符的准确性取决于将面部图像的本地邻域中存在的关系映射到微结构中的关系。在本文中，提出了一种局部梯度六到模式（LGHP），其识别在不同衍生方向上的不同距离处的参考像素和其相邻像素之间的关系。歧视信息存在于局部邻域以及不同的衍生方向上。所提出的描述符有效地将这些关系改变为判别具有最佳精度的二元微型图像。所提出的描述符的识别和检索性能已经与最先进的描述符相比，即最具挑战性和基准面部图像数据库的LDP和LVP，即裁剪延伸的Yale-B，CMU-Pie，Color-Feret和LFW。与最先进的描述符相比，所提出的描述符具有更好的识别以及检索速率。

在本文中，提出了R-Theta本地邻域模式（RTLNP），用于面部图像检索。 RTLNP以不同的角度和径向宽度在参考像素的本地附近的像素中利用关系。所提出的编码方案将本地邻域分成相等角度宽度的扇区。这些扇区再次分为两个径向宽度的子区。这些两个子区的平均灰度值被编码以生成微图案。已经评估了所提出的描述符的性能，并将结果与​​艺术描述符的状态进行比较。 LBP，LTP，CSLBP，CSLTP，Sobel-LBP，LTCOP，LMEP，LDP，LTRP，MBLBP，Brint和SLBP。最具挑战性的面部受限制和无约束数据库，即; AT＆T，Caria-Face-V5裁剪，LFW和彩色机构已被用于显示所提出的描述符的效率。建议的描述符也在近红外（NIR）面部数据库上进行测试; Casia Nir-Vis 2.0和Polyu-Nirfd探讨了它对NIR面部图像的潜力。与现有技术描述符相比，RTLNP的更好检索率显示了描述符的有效性

随机梯度体面（SGD）是深神经网络成功背后的核心技术之一。梯度提供有关功能具有最陡变化率的方向的信息。基本SGD的主要问题是通过梯度行为而对所有参数的相等大小的步骤进行更改。因此，深度网络优化的有效方式是为每个参数进行自适应步骤尺寸。最近，已经进行了几次尝试，以改善梯度下降方法，例如Adagrad，Adadelta，RMSProp和Adam。这些方法依赖于平方过去梯度的指数移动平均线的平方根。因此，这些方法不利用梯度的局部变化。在本文中，基于当前和立即梯度（即，差异）之间的差异提出了一种新颖的优化器。在所提出的差异优化技术中，以这样的方式调整步长，使得它应该具有更大的梯度改变参数的较大步长，以及用于较低梯度改变参数的较低步长。收敛分析是使用在线学习框架的遗憾方法完成。在本文中进行严格的分析超过三种合成复合的非凸功能。图像分类实验也在CiFar10和CiFAR100数据集上进行，以观察漫反射的性能，相对于最先进的优化器，例如SGDM，Adagrad，Adadelta，RMSProp，Amsgrad和Adam。基于基于单元（Reset）的基于卷积神经网络（CNN）架构用于实验中。实验表明，Diffgrad优于其他优化器。此外，我们表明差异对使用不同的激活功能训练CNN的均匀良好。源代码在https://github.com/shivram1987/diffgrad公开使用。

A framework for creating and updating digital twins for dynamical systems from a library of physics-based functions is proposed. The sparse Bayesian machine learning is used to update and derive an interpretable expression for the digital twin. Two approaches for updating the digital twin are proposed. The first approach makes use of both the input and output information from a dynamical system, whereas the second approach utilizes output-only observations to update the digital twin. Both methods use a library of candidate functions representing certain physics to infer new perturbation terms in the existing digital twin model. In both cases, the resulting expressions of updated digital twins are identical, and in addition, the epistemic uncertainties are quantified. In the first approach, the regression problem is derived from a state-space model, whereas in the latter case, the output-only information is treated as a stochastic process. The concepts of It\^o calculus and Kramers-Moyal expansion are being utilized to derive the regression equation. The performance of the proposed approaches is demonstrated using highly nonlinear dynamical systems such as the crack-degradation problem. Numerical results demonstrated in this paper almost exactly identify the correct perturbation terms along with their associated parameters in the dynamical system. The probabilistic nature of the proposed approach also helps in quantifying the uncertainties associated with updated models. The proposed approaches provide an exact and explainable description of the perturbations in digital twin models, which can be directly used for better cyber-physical integration, long-term future predictions, degradation monitoring, and model-agnostic control.

Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal's competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence.

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.