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This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

The purpose of this paper is to alleviate the problem of poor robustness and over-fitting caused by large-scale data in collaborative filtering recommendation algorithms.

Interpreting user behavior from the probabilistic perspective of hidden variables is helpful to improve robustness and over-fitting problems. Constructing a recommendation network by variational inference can effectively solve the complex distribution calculation in the probabilistic recommendation model. Based on the aforementioned analysis, this paper uses variational auto-encoder to construct a generating network, which can restore user-rating data to solve the problem of poor robustness and over-fitting caused by large-scale data. Meanwhile, for the existing KL-vanishing problem in the variational inference deep learning model, this paper optimizes the model by the KL annealing and Free Bits methods.

The effect of the basic model is considerably improved after using the KL annealing or Free Bits method to solve KL vanishing. The proposed models evidently perform worse than competitors on small data sets, such as MovieLens 1 M. By contrast, they have better effects on large data sets such as MovieLens 10 M and MovieLens 20 M.

This paper presents the usage of the variational inference model for collaborative filtering recommendation and introduces the KL annealing and Free Bits methods to improve the basic model effect. Because the variational inference training denotes the probability distribution of the hidden vector, the problem of poor robustness and overfitting is alleviated. When the amount of data is relatively large in the actual application scenario, the probability distribution of the fitted actual data can better represent the user and the item. Therefore, using variational inference for collaborative filtering recommendation is of practical value.

In the field of heritage science, especially applied to buildings and artefacts made by organic hygroscopic materials, analyzing the microclimate has always been of extreme importance. In particular, in many cases, the knowledge of the outdoor/indoor microclimate may support the decision process in conservation and preservation matters of historic buildings. This knowledge is often gained by implementing long and time-consuming monitoring campaigns that allow collecting atmospheric and climatic data.

Sometimes the collected time series may be corrupted, incomplete and/or subjected to the sensors' errors because of the remoteness of the historic building location, the natural aging of the sensor or the lack of a continuous check of the data downloading process. For this reason, in this work, an innovative approach about reconstructing the indoor microclimate into heritage buildings, just knowing the outdoor one, is proposed. This methodology is based on using machine learning tools known as variational auto encoders (VAEs), that are able to reconstruct time series and/or to fill data gaps.

The proposed approach is implemented using data collected in Ringebu Stave Church, a Norwegian medieval wooden heritage building. Reconstructing a realistic time series, for the vast majority of the year period, of the natural internal climate of the Church has been successfully implemented.

The novelty of this work is discussed in the framework of the existing literature. The work explores the potentials of machine learning tools compared to traditional ones, providing a method that is able to reliably fill missing data in time series.

The electromechanical brake system is leading the latest development trend in railway braking technology. The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder. The tolerance leads to imprecise brake control, so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system. This paper aims to present improved variational mode decomposition (VMD) algorithm, which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.

The VMD algorithm plays a pivotal role in the preliminary phase, employing mode decomposition techniques to decompose the motor speed signals. Afterward, the error energy algorithm precision is utilized to extract abnormal features, leveraging the practical intrinsic mode functions, eliminating extraneous noise and enhancing the signal’s fidelity. This refined signal then becomes the basis for fault analysis. In the analytical step, the cepstrum is employed to calculate the formant and envelope of the reconstructed signal. By scrutinizing the formant and envelope, the fault point within the electromechanical brake system is precisely identified, contributing to a sophisticated and accurate fault diagnosis.

This paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake (EMB) motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction. The signal is reconstructed according to the effective intrinsic mode functions (IMFS) component of removing noise, and the formant and envelope are calculated by cepstrum to locate the fault point. Experiments show that the empirical mode decomposition (EMD) algorithm can effectively decompose the original speed signal. After feature extraction, signal enhancement and fault identification, the motor mechanical fault point can be accurately located. This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.

By using this improved VMD algorithm, the electromechanical brake system can precisely identify the rotational anomaly of the motor. This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled. Compared with the conventional motor diagnosis method, this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs. Moreover, the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.

The purpose is to develop search and detection strategies that maximize the probability of detection of mine-like objects.

The author have developed a methodology that incorporates variational calculus, number theory and algebra to derive a globally optimal strategy that maximizes the expected probability of detection.

The author found a set of look angles that globally maximize the probability of detection for a general class of mirror symmetric targets.

The optimal strategies only maximize the probability of detection and not the probability of identification.

In the context of a search and detection operation, there is only a limited time to find the target before life is lost; hence, improving the chance of detection will in real terms be translated into the difference between success or failure, life or death. This rich field of study can be applied to mine countermeasure operations to make sure that the areas of operations are free of mines so that naval operations can be conducted safely.

There are two novel elements in this paper. First, the author determine the set of globally optimal look angles that maximize the probability of detection. Second, the author introduce the phenomenon of concordance between sensor images.

Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.

Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.