Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

A flexible ultra-broadband multi-layered absorber working at 2 GHz-40 GHz printed by resistive ink

A flexible extra broadband metamaterial absorber(MMA)stacked with five layers working at 2 GHz–40 GHz is investigated.Each layer is composed of polyvinyl chloride(PVC),polyimide(PI),and a frequency selective surface(FSS),which is printed on PI using conductive ink.To investigate this absorber,both one-dimensional analogous circuit analysis and three-dimensional full-wave simulation based on a physical model are provided.Various crucial electromagnetic properties,such as absorption,effective impedance,complex permittivity and permeability,electric current distribution and magnetic field distribution at resonant peak points,are studied in detail.Analysis shows that the working frequency of this absorber covers entire S,C,X,Ku,K and Ka bands with a minimum thickness of 0.098λ_(max)(λ_(max) is the maximum wavelength in the absorption band),and the fractional bandwidth(FBW)reaches 181.1%.Moreover,the reflection coefficient is less than-10 dB at 1.998 GHz–40.056 GHz at normal incidence,and the absorptivity of the plane wave is greater than 80%when the incident angle is smaller than 50°.Furthermore,the proposed absorber is experimentally validated,and the experimental results show good agreement with the simulation results,which demonstrates the potential applicability of this absorber at 2 GHz–40 GHz.

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Evaluation of soil erosion vulnerability in Hubei Province of China using RUSLE model and combination weighting method

Soil erosion has been recognized as a critical environmental issue worldwide.While previous studies have primarily focused on watershed-scale soil erosion vulnerability from a natural factor perspective,there is a notable gap in understanding the intricate interplay between natural and socio-economic factors,especially in the context of spatial heterogeneity and nonlinear impacts of human-land interactions.To address this,our study evaluates the soil erosion vulnerability at a provincial scale,taking Hubei Province as a case study to explore the combined effects of natural and socio-economic factors.We developed an evaluation index system based on 15 indicators of soil erosion vulnerability:exposure,sensitivity,and adaptability.In addition,the combination weighting method was applied to determine index weights,and the spatial interaction was analyzed using spatial autocorrelation,geographical temporally weighted regression and geographical detector.The results showed an overall decreasing soil erosion intensity in Hubei Province during 2000 and 2020.The soil erosion vulnerability increased before 2000 and then.The areas with high soil erosion vulnerability were mainly confined in the central and southern regions of Hubei Province(Xiantao,Tianmen,Qianjiang and Ezhou)with obvious spatial aggregation that intensified over time.Natural factors(habitat quality index)had negative impacts on soil erosion vulnerability,whereas socio-economic factors(population density)showed substantial spatial variability in their influences.There was a positive correlation between soil erosion vulnerability and erosion intensity,with the correlation coefficients ranging from-0.41 and 0.93.The increase of slope was found to enhance the positive correlation between soil erosion vulnerability and intensity.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

A sub-grid scale model for Burgers turbulence based on the artificial neural network method

The present study proposes a sub-grid scale model for the one-dimensional Burgers turbulence based on the neuralnetwork and deep learning method.The filtered data of the direct numerical simulation is used to establish thetraining data set,the validation data set,and the test data set.The artificial neural network(ANN)methodand Back Propagation method are employed to train parameters in the ANN.The developed ANN is applied toconstruct the sub-grid scale model for the large eddy simulation of the Burgers turbulence in the one-dimensionalspace.The proposed model well predicts the time correlation and the space correlation of the Burgers turbulence.

Production Capacity Prediction Method of Shale Oil Based on Machine Learning Combination Model

The production capacity of shale oil reservoirs after hydraulic fracturing is influenced by a complex interplay involving geological characteristics,engineering quality,and well conditions.These relationships,nonlinear in nature,pose challenges for accurate description through physical models.While field data provides insights into real-world effects,its limited volume and quality restrict its utility.Complementing this,numerical simulation models offer effective support.To harness the strengths of both data-driven and model-driven approaches,this study established a shale oil production capacity prediction model based on a machine learning combination model.Leveraging fracturing development data from 236 wells in the field,a data-driven method employing the random forest algorithm is implemented to identify the main controlling factors for different types of shale oil reservoirs.Through the combination model integrating support vector machine(SVM)algorithm and back propagation neural network(BPNN),a model-driven shale oil production capacity prediction model is developed,capable of swiftly responding to shale oil development performance under varying geological,fluid,and well conditions.The results of numerical experiments show that the proposed method demonstrates a notable enhancement in R2 by 22.5%and 5.8%compared to singular machine learning models like SVM and BPNN,showcasing its superior precision in predicting shale oil production capacity across diverse datasets.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics.This paper presents a machine learning(ML)framework for the prediction of the stress-strain behaviour and shearinduced contact fabric evolution of an idealised granular material subject to triaxial shearing.The MLbased framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method(DEM)model of the granular materials,a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro-and macro-mechanical information,as well as a multi-layer perceptron(MLP)neural network which is trained and tested using the DEM-based datasets.The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response.The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the MLebased modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials,bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials.Lastly,a detailed comparison between the used MLP model and long short-term memory(LSTM)model was made from the perspective of technical algorithm,prediction accuracy,and computational efficiency.

Big Model Strategy for Bridge Structural Health Monitoring Based on Data-Driven, Adaptive Method and Convolutional Neural Network (CNN) Group

This study introduces an innovative“Big Model”strategy to enhance Bridge Structural Health Monitoring(SHM)using a Convolutional Neural Network(CNN),time-frequency analysis,and fine element analysis.Leveraging ensemble methods,collaborative learning,and distributed computing,the approach effectively manages the complexity and scale of large-scale bridge data.The CNN employs transfer learning,fine-tuning,and continuous monitoring to optimize models for adaptive and accurate structural health assessments,focusing on extracting meaningful features through time-frequency analysis.By integrating Finite Element Analysis,time-frequency analysis,and CNNs,the strategy provides a comprehensive understanding of bridge health.Utilizing diverse sensor data,sophisticated feature extraction,and advanced CNN architecture,the model is optimized through rigorous preprocessing and hyperparameter tuning.This approach significantly enhances the ability to make accurate predictions,monitor structural health,and support proactive maintenance practices,thereby ensuring the safety and longevity of critical infrastructure.

Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Research and Practice of the Blended Teaching Model of BOPPPS Teaching Method Under the Background of Digital Education: Taking Operations Research Course as an Example

The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participatory learning,Post-assessment,Summary)teaching method in the development of a blended teaching model for the Operations Research course under the background of digital education.In response to the characteristics of the course and the needs of the student group,the teaching design is reconstructed with a student-centered approach,increasing practical teaching links,improving the assessment and evaluation system,and effectively implementing it in conjunction with digital educational technology.This teaching model has shown significant effectiveness in the context of digital education,providing valuable experience and insights for the innovation of the Operations Research course.