Variational Model Research Articles

A Dataset of 3M Single-DOF Planar 4-, 6-, and 8-Bar Linkage Mechanisms With Open and Closed Coupler Curves for Machine Learning-Driven Path Synthesis

Abstract In recent years, there has been a strong interest in applying machine learning techniques to path synthesis of linkage mechanisms. However, progress has been stymied due to a scarcity of high-quality datasets. In this article, we present a comprehensive dataset comprising nearly three million samples of 4-, 6-, and 8-bar linkage mechanisms with open and closed coupler curves. Current machine learning approaches to path synthesis also lack standardized metrics for evaluating outcomes. To address this gap, we propose six key metrics to quantify results, providing a foundational framework for researchers to compare new models with existing ones. We also present a variational autoencoder-based model in conjunction with a k-nearest neighbor search approach to demonstrate the utility of our dataset. In the end, we provide example mechanisms that generate various curves along with a numerical evaluation of the proposed metrics.

Nucleation of fracture: The first-octant evidence against classical variational phase-field models

Abstract As a companion work to [1], this Note presents a series of simple formulae and explicit results that illustrate and highlight why classical variational phase-field models cannot possibly predict fracture nucleation in elastic brittle materials. The focus is on “tension-dominated” problems where all principal stresses are non-negative, that is, problems taking place entirely within the first octant in the space of principal stresses.

Fertility model evolution: A survey on mathematical models of age-specific fertility with application to Nepalese and Malaysian data

Fertility pattern analysis and modeling to smooth age-specific fertility rates (ASFRs) form a well-established research field that holds particular importance for Asian countries. In developed nations, ASFRs typically display a bimodal skewed fertility curve, whereas, in developing countries, they usually exhibit a unimodal skewed fertility curve that diverges from the normal one. For decades, demographic experts worldwide have been interested in creating models using deterministic and stochastic approaches to represent these fertility curves. In this regard, parametric and non-parametric models have been created, with the latter providing a better fit for ASFR data. This research investigates the evolution of fertility models aimed at smoothing ASFRs. It explores suitable alternative models for countries with fast-declining, unimodal, and skewed fertility curves of ASFRs, such as Nepal and Malaysia. Nepal’s fertility rate is transitioning from a high level toward the replacement rate (2.1) at the year 2021; meanwhile, Malaysia’s fertility rate (1.7) in the year 2021 has dropped below the replacement rate. Given the lack of a universally applicable model for ASFR pattern variation, this study proposes the Kumaraswamy log-logistic distribution as a promising model to represent the ASFRs of Nepal and Malaysia accurately. Various approaches, including the Akaike information criterion, and Bayesian information criterion, are employed to validate the fitting of the proposed model.

Study on the Control Effect of Borehole Gas Extraction in Coal Seams Based on the Stress–Seepage Coupling Field

In order to determine the reasonable parameters of high-gas and extra-thick coal seam drainage, considering the factors of the coal seam metamorphic degree, stress condition, gas occurrence state, and permeability dynamic change, the gas desorption, diffusion, and transport process of coal seam gas are analyzed. A secondary distribution model of coal around the borehole, a porosity variation model of coal around the borehole, a stress–seepage coupling model, a pore flow model of the pressure-driven transition flow zone, and a free molecular flow zone are established. Taking the gas drainage of Zhangcun Coal Mine of Lu’an Group as the research object, the influence of drilling hole diameter, coal seam permeability, gas original pressure, and other factors on the control range of coal seam drainage drilling is simulated by ANSYS Fluent 6.3.26. The results show that secondary stress distribution occurs in the coal seam drill hole under the action of lead stress, which leads to the change in porosity; the seepage zone, transition zone, molecular flow zone, and original rock stress zone are presented around the drill hole; and the range of influence of the drill hole is mainly based on the seepage zone and the transition zone, supplemented by the molecular flow zone. The control range of the drill hole is in a positive proportional relationship to the diameter of the drill hole, the porosity of the coal seam, and the original pressure of the gas.

The Prediction Model of Seismic Variation in Complex Terrain based on the BP Neural Network with Cavities

The Prediction Model of Seismic Variation in Complex Terrain based on the BP Neural Network with Cavities

Variational Type Graph Autoencoder For Denoising On Event Recommendation

Recommendations for events play a pivotal role in facilitating the discovery of upcoming intriguing events within Event-Based Social Networks (EBSNs). Previous research has established the crucial significance of mining contextual features and implicit relationships to enhance recommendation performance and alleviate data sparsity issues. However, the noise inherent in contextual features exacerbates data sparsity and hampers the ability of previous methods to explore implicit relationships for mitigating data sparsity. To address this challenge, we propose a variational type graph autoencoder model that attenuates the influence of noise in different types of context features by introducing type-specific latent variables. Firstly, we introduce a heterogeneous denoising convolution module composed of two components: 1) Denoising attention aggregation is proposed to mitigate the influence of noisy structures and uncover implicit relationships. 2) A heterogeneous normalization module leverages context features within the same type to alleviate the effects of noise in context features and data sparsity. Furthermore, we propose a learnable heterogeneous mixture prior that assists in assigning different priors to distinct types of latent variables, effectively modeling different types of contextual features. Through comprehensive experiments conducted on real-world datasets, we demonstrate the compelling performance of our model compared to state-of-the-art competitive approaches.

A deep learning method to integrate extracelluar miRNA with mRNA for cancer studies.

Extracellular miRNAs (exmiRs) and intracellular mRNAs both can serve as promising biomarkers and therapeutic targets for various diseases. However, exmiR expression data is often noisy, and obtaining intracellular mRNA expression data usually involves intrusive procedures. To gain valuable insights into disease mechanisms, it is thus essential to improve the quality of exmiR expression data and develop noninvasive methods for assessing intracellular mRNA expression. We developed CrossPred, a deep-learning multi-encoder model for the cross-prediction of exmiRs and mRNAs. Utilizing contrastive learning, we created a shared embedding space to integrate exmiRs and mRNAs. This shared embedding was then used to predict intracellular mRNA expression from noisy exmiR data and to predict exmiR expression from intracellular mRNA data. We evaluated CrossPred on three types of cancers and assessed its effectiveness in predicting the expression levels of exmiRs and mRNAs. CrossPred outperformed the baseline encoder-decoder model, exmiR or mRNA-based models, and variational autoencoder models. Moreover, the integration of exmiR and mRNA data uncovered important exmiRs and mRNAs associated with cancer. Our study offers new insights into the bidirectional relationship between mRNAs and exmiRs. The datasets and tool are available at https://doi.org/10.5281/zenodo.13891508.

Joint Learning of Volume Scheduling and Order Placement Policies for Optimal Order Execution

Order execution is an extremely important problem in the financial domain, and recently, more and more researchers have tried to employ reinforcement learning (RL) techniques to solve this challenging problem. There are a lot of difficulties for conventional RL methods to tackle the order execution problem, such as the large action space including price and quantity, and the long-horizon property. As naturally order execution is composed of a low-frequency volume scheduling stage and a high-frequency order placement stage, most existing RL-based order execution methods treat these stages as two distinct tasks and offer a partial solution by addressing either one individually. However, the current literature fails to model the non-negligible mutual influence between these two tasks, leading to impractical order execution solutions. To address these limitations, we propose a novel automatic order execution approach based on the hierarchical RL framework (OEHRL), which jointly learns the policies for volume scheduling and order placement. OEHRL first extracts the state embeddings at both the macro and micro levels with a sequential variational auto-encoder model. Based on the effective embeddings, OEHRL generates a hindsight expert dataset, which is used to train a hierarchical order execution policy. In the hierarchical structure, the high-level policy is in charge of the target volume and the low-level learns to determine the prices for a series of the allocated sub-orders from the high level. These two levels collaborate seamlessly and contribute to the optimal order execution policy. Extensive experiment results on 200 stocks across the US and China A-share markets validate the effectiveness of the proposed approach.

Variational spatial-temporal graph attention network for state monitoring and forecasting

With the popularity of smart devices, there has been extensive collection of data structured in graphs. Spatial graphs, in particular, have garnered significant interest owing to their diverse range of applications. In this paper, we focus on applying spatial graph model for state monitoring and forecasting, with special attention to transportation systems. In current spatial modeling approaches, understanding the structure of a spatial graph usually relies on the analysis of gathered spatial–temporal data. However, spatial graph data in real world often contains temporary factors that are not easily detected. In this paper, we propose a novel variational inference-based model VISTG, which integrates such dynamics into spatial–temporal learning of spatial graph modeling. Specifically, VISTG is primarily composed of several spatial–temporal learning blocks, each encompassing both temporal and spatial learning layers. The temporal learning layer is crafted to characterize the distributions of latent factors using a variational inference-based model, aiming to capture the dynamics within the data. Subsequently, the spatial learning layer utilizes graph attention networks to describe the correlation among nodes. Additionally, an adaptive fusion module is implemented to equalize the impact of diverse temporal patterns. Finally, comprehensive experiments are carried out on two real-world datasets. The results affirm the efficacy of our model.

Population-based in silico modeling of anatomical shape variation of the knee and its impact on joint loading in knee osteoarthritis.

Anatomical knee joint features and osteoarthritis (OA) severity are associated, however confirming causals link to altered knee loading is challenging. This study leverages statistical shape models (SSM) to investigate the relationship between joint shape/alignment and knee loading during gait in knee OA(KOA) patients to understand their contribution to elevated medial knee loading in OA. Musculoskeletal (MSK) models were created for the mean as well as the first eightSSM principal modes of variation (-3,-2,-1, +1, +2, +3 standard deviations for each mode) and used as input to a MSK modeling framework. Using an identical KOA gait pattern (i.e., joint kinematics and ground reaction forces), we ran simulations for each MSK model and evaluated medial compartment loading magnitude and contact distribution at the instant of first and second peak of knee joint loading. An increase in external rotation, posterior tibia translation and a decrease in medial joint space and medial femoral condylar size predisposed the medial compartment knee joint to overloading during gait. This was coupled with an anterior and medial shift in contact location with increasing external rotated tibial position and increasing posterior tibial translation with respect to the femur. Next, results also highlighted a posterior shift of the medial compartment loading location with decreasing medial joint space. This study provides important population-based insights on how knee shape and alignment predispose individuals with KOA to elevated medial compartmental knee loading. This information can be crucial in assessing the risk for medial KOA development and progression.

Probabilistic oil price forecasting with a variational mode decomposition-gated recurrent unit model incorporating pinball loss

Prediction methods have garnered significant attention in intelligent decision-making. Most existing approaches to predicting crude oil prices prioritize accuracy and stability while providing precise prediction intervals (PIs) that can offer valuable insights. Thus far, we introduce a novel hybrid model to forecast future crude oil prices. Our approach leverages the variational mode decomposition (VMD) to simplify the complexity of the original time series, yielding a set of subseries. These subseries are then modeled using a deep neural network architecture called a gated recurrent unit (GRU). To address the prediction uncertainty, we employed the pinball loss function rather than the mean square error (MSE) to guide the proposed VMD-GRU. This adaptation extends the traditional GRU-based point forecasting to probabilistic forecasting by estimating quantiles. We evaluated our proposed model on a well-established crude oil price series by conducting both single- and multi-step-ahead forecasting analyses. Our findings underscore the efficacy of the combined model, demonstrating its superior predictive performance compared to benchmark models.

Micromechanics-based variational phase-field modeling of fatigue fracture

In this paper, we extend the micromechanics-based phase-field model to simulate fatigue failure. The coupling of a micromechanics-based framework with the phase-field approach helps to differentiate between failure modes, by distinguishing between open and closed microcracks. This integrated framework links continuum field variables, such as plastic strain and damage variable, to micromechanical mechanisms like frictional sliding and microcrack opening. We first improve the algorithm’s stability during loading-unloading in the tensile regime through a modification of the plasticity evolution equations. Next, we incorporate fatigue damage accumulation and deterioration due to cyclic loading into the micromechanics-based phase-field model. A fatigue degradation function, driven by free energy accumulation, is introduced to degrade the fracture energy upon reaching a specified threshold during cyclic loading. Various cyclic loads are applied to benchmark tests, both with and without imperfections (e.g. holes, inclusions, voids), under plane strain conditions to capture diverse failure modes. The results demonstrate the model’s capability to accurately describe tensile, shear, and mixed-mode fracture under cyclic loading. Furthermore, the model effectively simulates key features of fatigue behavior, including crack nucleation, growth, and coalescence.

Long Duration Forecasting and its Performance Capability for Seasonal Variation Modelling of Residual Chlorine Concentrations: A Comparative Evaluation of two Small-scale Water Distribution Systems in Japan

Chlorine dosing control is a critical task for health security, complying with drinking water quality standards while achieving customer satisfaction. In Japan, this became more difficult due to decreasing number of technical personnel as a result of declining population and huge retirement of veterans. As experienced-based dosing control still exists and is considered inefficient due to risks of inaccurate dosing and need of experienced manpower, streamlining of operations is needed. This study aims to address these concerns through the development and evaluation of a deep learning model for residual chlorine concentrations capable of forecasting long durations. In this paper, the model is investigated in seasonal timeframe analyzing trends and variations. Two water distributions systems of varying network—simple and complex, are also compared to further analyze model performance and versatility. The model utilizes the past 24 hours of flow rate, chlorine level at treatment plant, water temperature, and residual chlorine at private homes as input to predict the 12 hours ahead of residual chlorine at private homes evaluated at hourly training lengths of 0.5, 1, 1.5, 2 years. Results revealed that the model achieved high accuracy in predicting hourly residual chlorine with general increasing model error from winter, spring, autumn, and summer due to the progressing instabilities in chlorine concentrations from low to high temperatures. Moreover, smaller system tends to be more unstable incurring lower model performance relative to larger system. In terms of optimal training length, ≥1Y training models are found to have lesser chance of data drift occurrence prospectively reducing model retraining frequency in the future.

Simulations and machine learning models for cosmic-ray short-term variations and test-mass charging on board LISA

Simulations and machine learning models for cosmic-ray short-term variations and test-mass charging on board LISA

Long-term changes of sodium column abundance at 24.6°S above the Atacama Desert in Chile

Aims. The utilisation of artificial laser guide star (LGS) obviates the necessity for a prominent natural guide star (NGS) within adaptive optics (AO) systems. High-power lasers are fundamental components of most AO systems today. The generation of an LGS relies on the excitation of sodium (denoted by its symbol Na) atoms situated in the upper atmosphere. Therefore, the sodium vertical column density (denoted as CNa) is a crucial parameter. Beyond ensuring the optimal and stable performance of an AO system, knowledge of the return flux from an LGS is imperative during the design phase, aiding in the accurate specification of both the LGS and the AO system. The availability of sodium in the upper atmosphere has been the focal point of diverse studies, exhibiting a pronounced dependence on the specific observatory site. Furthermore, it is well established that CNa varies across multiple timescales, including hours, nights, months, seasons, and even several years. As many of the world’s largest telescopes are located in the Atacama Desert in northern Chile, our objective is to provide CNa statistics pertinent to this specific region. Methods. We used telemetry data from the AO systems operational at the Paranal Observatory (24.6°S, 70.4°W): Ground Atmospheric Layer Adaptive Corrector for Spectroscopic Imaging (GALACSI) and Ground layer Adaptive Optics system Assisted by Lasers (GRAAL). We combined these data with measurements from two space instruments: SCanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) and Optical Spectrograph and Infrared Imaging System (OSIRIS), as well as with simulated data from the Whole Atmosphere Community Climate Model (WACCM). We carefully analysed and compared these datasets to develop a statistical model for the temporal variations of CNa. Results. We validated the use of the AO telemetry data from Paranal systems to retrieve the CNa. The near-continuous measurements encompassing the period from mid-2017 to the end of 2023 facilitated the determination of monthly and yearly abundance and variability of Na in the mesopause region. Throughout the complete years of measurement, the annual and semi-annual variations exhibit consistent characteristics that align with previously documented findings in atmospheric studies. Through meticulous comparison and the fitting of various long-term datasets, we formulated a model depicting the evolution of CNa over time. The validity of our data processing and model is scrutinised, and the results obtained for the Paranal latitude exhibit noteworthy concordance with the findings of other studies.

Prediction of Rubber Fatigue Life Using an Assimilation‐based Learning Approach and Incremental Crack Propagation Model

ABSTRACTAccurately and efficiently predicting the fatigue life of rubber materials has been a long‐standing challenge due to limited understanding of the fatigue mechanism. In this study, a variational assimilation‐based machine learning method assisted with incremental crack propagation model is proposed to predict the fatigue life of rubber materials. Firstly, according to the fracture mechanics theory, a new rubber fatigue life prediction model based on incremental crack propagation and sparse experimental data is established, which owns higher accuracy than the classical crack energy density model. Further, a rubber fatigue life solver coupled incremental crack propagation model and nonlinear finite element method is introduced to generate a dense fatigue life dataset of rubber materials with high accuracy. Finally, the artificial neural network model is trained, cross‐validated, and tested using the dense dataset, and the three‐dimensional variational assimilation model is employed to merge the predicted values of artificial neural network with experimental data. By comparing against the experimental data, the effectiveness of the proposed method was verified; thereby, we offer an accurate and efficient approach to predict the rubber fatigue life.

A hybrid variational level set model based on double Gaussian distribution fitting energy for image segmentation and bias correction

AbstractThe variational level set model has been widely used in image segmentation. However, its performance is significantly hindered by bias fields and noise within the images. To address these limitations, we introduce a novel hybrid variational level set model based on dual Gaussian distribution fitting (DGDF) energy in this paper. The DGDF energy integrates both local and global Gaussian distributions. The local energy is derived from the original image, while the global energy employs the corrected image, enabling effective segmentation of images with intensity inhomogeneity. Furthermore, the model demonstrates low sensitivity to weighting parameters and robust performance for noisy images. We develop an alternating iteration algorithm that combines variational methods with gradient descent to efficiently solve the proposed model. Experimental results validate the effectiveness of the model and the algorithm. In addition, the proposed model shows competitiveness on test images and three datasets compared to several state‐of‐the‐art models, including other variational level set models and deep learning‐based techniques.

Stream of variation modeling and monitoring for heterogeneous profiles in multi-stage manufacturing processes

ABTRACT Advanced manufacturing systems typically involve multiple operating stages, where in-process data are observed in the form of profiles that contain rich information for process monitoring. Emerging methodologies have been developed for multi-stage profile monitoring. However, the cases where different stages’ profiles are heterogeneous and variations propagate over stages have not been addressed so far. To this end, this article proposes a heterogeneous profiles-based stream of variation (HP-SoV) framework for multi-stage manufacturing process monitoring. It uses functional decomposition to extract features of heterogeneous profiles from different stages, where the decomposition coefficients are regarded as latent states that propagate along consecutive stages to capture the variation propagation. HP-SoV includes many existing models as its special cases, and enjoys an efficient inference algorithm via maximum likelihood estimation. Based on the one-step-ahead forecast errors of HP-SoV, a group monitoring scheme is further developed for online monitoring. Extensive numerical studies explore the modeling robustness and monitoring effectiveness of HP-SoV under different settings. A case study demonstrates the applicability of HP-SoV in multi-stage process monitoring for heterogeneous profiles.

PERAMALAN HARGA GULA PASIR MENGGUNAKAN VARIASI KALENDER REGARIMA DENGAN MOVING HOLIDAY EFFECT (PERIODE JANUARI 2018 SAMPAI DENGAN DESEMBER 2022 DI PASAR KOTA SEMARANG)

National sugar production is decreasing day by day with the pattern of people's consumption of sugar continuing to increase, thus encouraging the government to import sugar from other countries to meet food needs. This is because the import of granulated sugar causes the price of local granulated sugar to fluctuate which can rise up to 2 times the highest retail price. Eid al-Fitr is determined based on the Islamic calendar, this will cause a shift in the date each year on the Maseh calendar, the date of the celebration of Eid al-Fitr which moves from year to year is known as the "moving holiday effect". One of the calendar variation models used to eliminate the Holiday Effect Transfer and has a simple processing flow is the RegARIMA model. The RegARIMA model method is a modeling technique that combines the ARIMA model with the regression model. In the regression model, the weight matrix is used as the independent variable and the price of granulated sugar is used as the dependent variable. The weight value is obtained based on the number of days that affect Eid, which is 14 days. Based on an analysis of the price of granulated sugar in the Semarang City market for the period January 2018 to December 2022, the best model is obtained, namely SARIMA (1,0,0)12 with the smallest AIC value and the sMAPE value obtained from forecasting data for 2021 is of 19.04%, which means that the forecasting is still at a reasonable level.

A general framework for whiteness-based parameters selection in variational models

A general framework for whiteness-based parameters selection in variational models