Analysis of a Dynamic Viscoelastic Contact Problem with Normal Compliance, Normal Damped Response, and Nonmonotone Slip Rate Dependent Friction by Mikaël Barboteu, David Danan

“…Next, we introduce a fully discrete approximation of the variational problem based on a finite element method and on an implicit time integration scheme. …”
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VIM-Based Dynamic Sparse Grid Approach to Partial Differential Equations by Shu-Li Mei

“…Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. …”
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Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost by Shu-Li Mei

“…Second, using the couple technique of the variational iteration method (VIM) and the precision integration method, the sparse approximation solution of the nonlinear partial differential equations can be obtained. …”
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Hybrid energy storage systems for photovoltaic storage microgrids power allocation and capacity determination based on adaptive Savitzky-Golay filtering and VMD-DTW by Zengqiang Ma, Zejia Zhou, Tianming Mu, Cheng Wen

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P-V-L Deep: A Big Data Analytics Solution for Now-casting in Monetary Policy by Maryam Hajipour Sarduie, Mohammadali Afshar Kazemi, Mahmood Alborzi, Adel Azar, Ali Kermanshah

“…The main scientific contribution of this article is presenting a new approach of policy-making for the now-casting of economic indicators in order to improve the performance of forecasting through the combination of deep nets and deep learning methods in the data and features representation. In this regard, a net under the title of P-V-L Deep: Predictive Variational Auto Encoders - Long Short-term Memory Deep Neural Network was designed in which the architecture of variational auto-encoder was used for unsupervised learning, data representation, and data reconstruction; moreover, long short-term memory was adopted in order to evaluate now-casting performance of deep nets in time-series of macro-econometric variations. …”
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Optimal Consumption, Leisure, and Investment with Partial Borrowing Constraints over a Finite Horizon by Geonwoo Kim, Junkee Jeon

“…We provide an integral equation representation of the free boundary and solve it numerically via a recursive integration method. …”
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A Hybrid Model for Carbon Price Forecasting Based on Secondary Decomposition and Weight Optimization by Yongfa Chen, Yingjie Zhu, Jie Wang, Meng Li

“…The empirical results of the carbon markets in Hubei and Guangdong indicate that the proposed method outperforms the benchmark model in terms of prediction accuracy and robustness, and the method has been tested by Diebold Mariano (DM). …”
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A secure IoT-edge architecture with data-driven AI techniques for early detection of cyber threats in healthcare by Mamta Kumari, Mahendra Gaikwad, Salim A. Chavan

“…This work proposes a fresh classification of an attack detection algorithm for IoMT, as well as a method comparison and dataset categorization to improve detection performance. …”
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Interpretable artificial intelligence (AI) for cervical cancer risk analysis leveraging stacking ensemble and expert knowledge by Priyanka Roy, Mahmudul Hasan, Md Rashedul Islam, Md Palash Uddin

“…Generative artificial intelligence methods, such as variational autoencoders and generative teaching networks, were evaluated but showed suboptimal performance. …”
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Robust Adaptive Multiple Backtracking VBKF for In-Motion Alignment of Low-Cost SINS/GNSS by Weiwei Lyu, Yingli Wang, Shuanggen Jin, Haocai Huang, Xiaojuan Tian, Jinling Wang

“…To address the issue that low-cost SINS/GNSS cannot effectively achieve rapid and high-accuracy alignment in complex environments that contain noise and external interference, an adaptive multiple backtracking robust alignment method is proposed. The sliding window that constructs observation and reference vectors is established, which effectively avoids the accumulation of sensor errors during the full integration process. …”
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Enhancing Planning for Autonomous Driving via an Iterative Optimization Framework Incorporating Safety-Critical Trajectory Generation by Zhen Liu, Hang Gao, Yeting Lin, Xun Gong

“…To generate safety-critical trajectories, the decoder within the conditional variational auto-encoder (CVAE) is innovatively designed through a data-mechanism integration method, ensuring that these trajectories strictly adhere to vehicle kinematic constraints. …”
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Measuring. Monitoring. Management. Control by A.J. Alieva, Kh.S. Alieva, M.G. Ashrafov, N.Kh. Mustafazade

“…Results. Using the variational optimization method, the optimal type of the specified dependence is calculated. …”

On the Fractional Nagumo Equation with Nonlinear Diffusion and Convection by Abdon Atangana, Suares Clovis Oukouomi Noutchie

“…Both methods use a basic idea of integral transform and are very simple to be used.…”
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Chaotic and quasi-periodic dynamics in fractional-order nonlinear wave systems within dispersive-dissipative media by Wael W Mohammed, Fakhr Gassem, Rabeb Sidaoui, Aleksander Vokhmintsev, Mostafa M. A. Khater

“…Through the complementary application of the Khater III method and an enhanced Kudryashov technique, we derive closed-form solutions and rigorously validate them via numerical implementation of He’s variational iteration approach. …”
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Electric load forecasting based on kernel extreme learning machine optimized by improved sparrow search algorithm by Diming Zhang, Yuchen Xu, Yuanjiang Li

“…Consequently, the proposed method offers more accurate forecasting, contributing to the safe and stable operation of power systems.…”
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Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport by Cécile Barbachoux, Joseph Kouneiher

“…We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. …”
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Application of PFI-4DVar Data Assimilation Technique to Nowcasting of Numerical Model by Jiang Wenjing, Liang Xudong

“…And appropriate data assimilation technology can be used to produce a more accurate initial field, making the integral forecast results closer to the reality. The PFI-4DVar assimilation method (four-dimensional variational technology under physical filter initialization) can filter in the process of assimilation rather than model integration, thus shortening the model spin-up time and getting a more dynamic and physically coordinated analysis field. …”
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Simultaneous Vibration and Nonlinearity Compensation for One-Period Triangular FMCW Ladar Signal Based on MSST by Wei Li, Ruihua Shi, Qinghai Dong, Juanying Zhao, Bingnan Wang, Maosheng Xiang

“…To solve these problems, this paper proposes a compensation method combining multiple synchrosqueezing transform (MSST), equal-phase interval resampling, and high-order ambiguity function (HAF). …”
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A data-driven hybrid framework for voltage transformer ratio error prediction: Addressing challenges in complex power systems by Jiuxi Cui, Zhenhua Li, Heping Lu, Feng Zhou, Haoyu Chen, Zhenxing Li

“…First, an energy entropy-optimized adaptive variational mode decomposition method is developed, which introduces convergence constraints for parameter selection, reducing randomness during the decomposition process and is validated by power spectrum analysis. …”
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Multiple Solutions for a Class of Fractional Boundary Value Problems by Ge Bin

“…The approach used in this paper is the variational method. More precisely, the Weierstrass theorem and mountain pass theorem are used to prove the existence of at least two nontrivial solutions.…”
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