Modeling Problems Research Articles

Pattern‐moving‐based dynamic description and optimal control for non‐Newtonian mechanical systems with generalized cell mapping

AbstractThis article focuses on the problem of modelling and control for a non‐Newtonian mechanical system that may be subject to the statistical law instead of the traditional Newtonian principles mechanics. A discrete method, synthesizing the generalized cell mapping (GCM) together with dynamic programming (DP), with inverse search strategy, using pattern moving theory (PMT) framework, was proposed. The basic idea is to describe and control the system's dynamic peculiarity utilizing pattern class variable in ‘pattern moving space’. First, a few prior concepts were reviewed, including PMT, cell mapping, and optimal control for this kind system. Then, we articulated a cross‐mapping method to analyze the system dynamic behaviour, which takes into account the computational and statistical properties of pattern class variable simultaneously. For system optimal control, the improved GCM and cost function were performed to determine the discrete optimal control table (DOCT) in accordance with dynamic programming and inverse search. Finally, simulation results of two cases demonstrate the efficiency and practicality of the proposed approach. The study has resulted in a solution of describing and controlling based on pattern class variable for non‐Newtonian mechanical systems, and its main objective was to give a different perspective in term of research into non mechanistic principles modelling and application of nonlinear systems.

Transfer learning enabled transformer-based generative adversarial networks for modeling and generating terahertz channels

Terahertz communications are envisioned as a promising technology for the sixth generation and beyond wireless systems, which can support wireless links with Terabits-per-second (Tbps) data rates. As the foundation of designing terahertz communications, channel modeling and characterization are crucial to scrutinize the potential of this spectrum. However, current channel modeling in the terahertz band heavily relies on time-consuming and costly measurements. Here, we propose a transfer learning enabled transformer based generative adversarial network to mitigate this problem in terahertz channel modeling. Specifically, as a fundamental building block, a generative adversarial network is exploited to generate channel parameters. To improve the accuracy, a transformer structure with a self-attention mechanism is incorporated in generative adversarial network. Still incurring errors compared with ground-truth measurement, a transfer learning is designed to solve the mismatch between the formulated network and measurement. The proposed method can achieve high accuracy in channel modeling, while requiring only rather limited amount of measurement, which is a promising complement of current channel modeling techniques.

Modeling of the discharge coefcient of diferential pressure fowmeters: approximation by using radial-basis function neural networks

The discharge coefficient of flow transducers of liquids and gases of differential pressure flowmeters plays an important role in flow rate measurement. The problem of modeling and calculating the discharge coefficient of differential pressure flowmeters directly affects the accuracy of flow rate measurement of these devices. The results of modeling the discharge coefficient of the differential pressure flowmeter in the form of radial-basis neural networks are presented. The described structure of the neural network calculates the values of the discharge coefficient with an angular pressure tapping method. The article evaluates the error of approximation of the discharge coefficient by radial-basis function networks and provides recommendations for building such networks to solve problems of modeling the characteristics of differential pressure flowmeters. The article discusses the main advantages and disadvantages of using such networks as discharge coefficients of the differential pressure flowmeters. The research showed that the use of such networks is justified by their properties to approximate the discharge coefficient and their efficiency in measuring gas and liquid flow rates.

An improved goal-oriented adaptive finite-element method for 3-D direct current resistivity anisotropic forward modeling using nested tetrahedra

We developed a novel adaptive finite element method (FEM) to address the problem of 3-D direct current (DC) resistivity forward modeling with complex surface topography and arbitrary conductivity anisotropy. The tetrahedra-based FEM and secondary virtual potential algorithm are first used to handle arbitrary complex geo-models. Then, to ensure the accuracy of the simulation solution, an improved goal-oriented adaptive mesh refinement (AMR) algorithm is proposed to realize an optimized mesh density distribution. To avoid the drawback of the traditional goal-oriented AMR algorithm for the DC forward modeling problem, we incorporate a volume-based weighting factor into the posterior error estimation procedure to further optimize the density distribution of the forward modeling grid. In addition, instead of traditional open source mesh generation software, we propose using the longest-edge bisection (LEB) algorithm to perform the mesh refinement process, which can preserve the topological structure between different-level meshes. Finally, the comprehensive test using a two-layered model and two complex 3-D models demonstrate the capability of our newly developed code to obtain highly accurate solutions even on relatively coarse initial grids. By incorporating the volume factor, our novel AMR algorithm achieves a more uniform and reasonable mesh density distribution during these experiments. The LEB refinement technique can generate a series of nested tetrahedral elements and provide fewer tetrahedral elements compared to the traditional Delaunay-based AMR method. The proposed 3-D DC forward modeling method has been implemented into an open source C++ code, which will contribute to the advancement of the 3-D DC resistivity imaging field.

The optimal tennis serve: a mathematical model

Mathematical modelling has several valuable properties that address a number of pedagogical issues. As such, it makes for an excellent classroom exercise. First and foremost, it reinforces the insight that mathematics is nearly ubiquitous. It is all around us, hiding in plain sight. Secondly, in contrast to textbook problems which are often highly artificial, mathematical modelling is decidedly real. Next, it serves to un-silo the curriculum. As mathematics students advance, they populate their toolbox with more and more tools. However, these tools are generally course specific. Algebra tools in algebra class, calculus tools in calculus class, and so on. In attacking a modelling problem, the student needs to decide what tool to pick up and how to apply it. Finally, modelling is empowering in that it allows, indeed it requires, the student to decide for herself what the salient features of a problem are and which features are extraneous and can safely be suppressed.

The Problem of Differential Importability and Scientific Modeling

The practice of science appears to involve “model-talk”. Scientists, one thinks, are in the business of giving accounts of reality. Scientists, in the process of furnishing such accounts, talk about what they call “models”. Philosophers of science have inspected what this talk of models suggests about how scientific theories manage to represent reality. There are, it seems, at least three distinct philosophical views on the role of scientific models in science’s portrayal of reality: the abstractionist view, the indirect fictionalist view, and the direct fictionalist view. In this essay, I try to articulate a question about what makes a scientific model more or less appropriate for a specific domain of reality. More precisely, I ask, “What accounts for the fact that given a determinate target domain, some scientific models, but not others, are thought to be “appropriate” for that domain?” I then consider whether and the degree to which each of the mentioned views on scientific models institutes a satisfactory response to this question. I conclude that, amongst those views, the direct fictionalist view seems to have the most promising response. I then utilize this argument to develop a more precise account of the problem of differential importability, and ultimately offer a more general and less presumptive argument that the problem seems to be optimally solved by justifying comparative evaluation of model-importabilities solely in terms of comparative evaluations of what I characterize as models’ “holistic” predictive success.

Constraint Realization‐Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

ABSTRACTIn this article, we first introduce a Hamel field integrator designed for a geometrically exact Euler–Bernoulli beam with infinite‐dimensional holonomic constraints, constructed using a Lagrange multiplier. This method addresses the complexities introduced by constraints, but the additional multiplier introduces a new degree of freedom and hence results in a system with mixed‐type partial differential equations. To address this issue, we further propose a constraint realization method based on perturbation theory for infinite‐dimensional mechanical systems within the framework of Hamel's formalism. This method circumvents the use of additional Lagrange multiplier, significantly reducing the computational complexity of modeling problems. Building on this, we construct a perturbed Hamel field integrator optimized for parallel computing and incorporate artificial viscosity to accelerate constraint convergence. While applicable to three dimensions, our method is demonstrated in a simplified context using planar Euler–Bernoulli beam examples to illustrate the effectiveness of the unified mathematical framework.

PEDAQOJİ ELMDƏ MODELLƏŞDİRMƏ PROBLEMLƏRİ: TƏHLİL VƏ PERSPEKTİVLƏR

Problems of modeling in pedagogical science are a serious challenge for scientists and practitioners in the field of education. However, through joint efforts and the development of new methodologies, we can overcome these obstacles and create more accurate and effective models that contribute to improving the quality of education and the successful development of students.

Hypergraph contrastive attention networks for hyperedge prediction with negative samples evaluation

Hyperedge prediction aims to predict common relations among multiple nodes that will occur in the future or remain undiscovered in the current hypergraph. It is traditionally modeled as a classification task, which performs hypergraph feature learning and classifies the target samples as either present or absent. However, these approaches involve two issues: (i) in hyperedge feature learning, they fail to measure the influence of nodes on the hyperedges that include them and the neighboring hyperedges, and (ii) in the binary classification task, the quality of the generated negative samples directly impacts the prediction results. To this end, we propose a Hypergraph Contrastive Attention Network (HCAN) model for hyperedge prediction. Inspired by the brain organization, HCAN considers the influence of hyperedges with different orders through the order propagation attention mechanism. It also utilizes the contrastive mechanism to measure the reliability of attention effectively. Furthermore, we design a negative sample generator to produce three different types of negative samples. We evaluate the impact of various negative samples on the model and analyze the problems of binary classification modeling. The effectiveness of HCAN in hyperedge prediction is validated by experimentally comparing 12 baselines on 9 datasets. Our implementations will be publicly available at https://github.com/jianruichen/HCAN.

Modified Hermite Wavelet Discrete Matrix Approach for the Brusselator Chemical Model

AbstractThe primary goal of this study is to create a wavelet collocation technique that can be used to solve nonlinear fractional order systems of ordinary differential equations, which are equations that arise in modeling problems related to auto‐catalytic chemical reactions. Using the Hermite wavelet collocation method (HWCM), the system of nonlinear ordinary differential equations of integer and fractional order is numerically solved. The nonlinear Brusselator system is transformed into an algebraic equation system using the collocation method and the fractional derivative operational matrices. The Newton‐Raphson method is used to solve these algebraic equations, and the approximate values of the derived unknown coefficients are substituted. Through the numerical examples, the method's computational effectiveness and correctness are illustrated with various model constraints. A numerical comparison is made between the current approach ND solver, RK method, and Haar wavelet method (HWM). The efficiency and reliability of the developed strategy's performance are shown in graphs and tables. The created Hermite wavelet collocation method is resilient and has good accuracy compared to current methods found in the literature. Numerical computations are performed through Mathematica, a mathematical software.

The problem of social modeling of the activity of youth online communities in the context of social and political mobilization

The problem of social modeling of the activity of youth online communities in the context of social and political mobilization

AnFiS-MoH: Systematic exploration of hybrid ANFIS frameworks via metaheuristic optimization hybridization with evolutionary and swarm-based algorithms

The adaptive neuro-fuzzy inference system (ANFIS) has shown promising performance in modeling nonlinear problems, leveraging the strengths of both neural networks and fuzzy inference systems. However, as the problem scale increases, the growing number of tunable parameters in ANFIS can make it challenging to optimize via traditional gradient-based methods alone. This study introduces AnFiS-MoH, a novel framework that synergistically integrates ANFIS with metaheuristic optimization algorithms to address these challenges. By leveraging the global search capabilities of metaheuristics such as ant colony optimization (ACO), particle swarm optimization (PSO), genetic algorithm (GA), and simulated annealing (SA), ANFIS-MOH enhances the parameter tuning process of ANFIS models. We evaluate ANFIS-MOH on benchmark datasets including Boston Housing and Wine Quality, demonstrating significant improvements in prediction accuracy and generalization compared to traditional ANFIS and neural network approaches. The proposed framework achieves up to 20% reduction in Mean Squared Error and 15% increase in R2 scores, particularly excelling in handling high-dimensional, noisy data. This work contributes to the field of hybrid intelligent systems by introducing effective ways to combine the strengths of ANFIS with powerful metaheuristic optimization algorithms. The findings suggest that such hybrid approaches can be effective in tackling challenging nonlinear modeling problems. Our code is available at https://github.com/AmbitYuki/Metaheuristic-Adaptive-ANFIS.

Developing modelling competencies in pre-service mathematics teachers through reflective thinking skills

Background: Ghana’s commitment to quality education has been reflected in its goal of providing equal access to high-quality education, leading to the reforms of the New Common Core Mathematics Curriculum for Basic Schools. The study explored the integration of mathematical modelling using reflective thinking skills, which are not currently core competencies in Ghanaian basic school curriculum.Aim: The study examined the modelling proficiency of pre-service mathematics teachers by assessing their reflective thinking abilities in a modelling laboratory context.Setting: The study focussed on pre-service mathematics teachers from two education colleges in Ghana.Methods: Using purposive sampling to select participants, a quasi-experimental design with pre- and post-test interventions was employed. Data were analysed through content and inferential analysis, supplemented by interviews.Findings: The findings indicated that the comparison group lacked prior knowledge of modelling problems and struggled with comprehension tasks. In contrast, the experimental group successfully translated real-world problems into mathematical models.Conclusion: Providing pre-service mathematics teachers access to a modelling laboratory and modelling-eliciting activities was essential for developing future modellers. This approach would enhance their effectiveness in teaching foundational mathematics in Ghanaian education.Contribution: This study advocated for re-orienting the mathematics curriculum at both Basic schools and Colleges of Education in Ghana to include mathematical modelling and reflective thinking skills as core components.

Flight Arrival Scheduling via Large Language Model

The flight arrival scheduling problem is one of the critical tasks in air traffic operations, aiming to ensure that the flight arrive in the correct sequence safely. Existing methods primarily focus on the terminal area and often overlook the presence of training flight at the airport. Due to the limited generalization of traditional methods and varying control practices at different airports, training flight at airports still rely on manual control for arrival sorting. To effectively address these issues, we propose a novel method for slot allocation that leverages the strong reasoning capabilities and generalization potential of large language models (LLMs). Our method conceptualizes the dynamic scheduling problem for training flight as a language modeling problem, a perspective not previously explored. Specifically, we represent the allocator’s inputs and outputs as language tokens, utilizing LLMs to generate conflict-free results based on a language description of requested landing information and assigned training flight information. Additionally, we employ a reset strategy to create a small dataset for scenario-specific samples, enabling LLMs to quickly learn allocation schemes from the dataset. We demonstrated the capability of LLMs in addressing time conflicts by evaluating metrics such as answer accuracy, conflict rate, and total delay time (without the wrong answer). These findings underscore the feasibility of employing LLMs in the field of air traffic control.

Exact Solutions to Some Thermokarst Modeling Problems

Exact Solutions to Some Thermokarst Modeling Problems

A Bayesian hybrid method for the analysis of generalized linear models with missing-not-at-random covariates

Missing data handling is one of the main problems in modelling, particularly if the missingness is of type missing-not-at-random (MNAR) where missingness occurs due to the actual value of the observation. The focus of the current article is generalized linear modelling of fully observed binary response variables depending on at least one MNAR covariate. For the traditional analysis of such models, an individual model for the probability of missingness is assumed and incorporated in the model framework. However, this probability model is untestable, as the missingness of MNAR data depend on their actual values that would have been observed otherwise. In this article, we consider creating a model space that consist of all possible and plausible models for probability of missingness and develop a hybrid method in which a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is combined with Bayesian Model Averaging (BMA). RJMCMC is adopted to obtain posterior estimates of model parameters as well as probability of each model in the model space. BMA is used to synthesize coefficient estimates from all models in the model space while accounting for model uncertainties. Through a validation study with a simulated data set and a real data application, the performance of the proposed methodology is found to be satisfactory in accuracy and efficiency of estimates.

Modeling of seismic wave scattering in poroelastic media

Understanding wave scattering in the earth is considered fundamental in describing seismic wave propagation and providing information on structural features of the earth’s interior. Petrophysical parameters (especially porosity and permeability) affect the reflection coefficients of subsurface interfaces, which can better explain the field data and infer the subsurface structure. However, the numerical solutions to the scattering problem for efficient modeling of wave propagation in poroelastic earth structures have limitations. We develop a numerical algorithm for solving the poroelastic scattering integral equations. Specifically, applying perturbation theory to Biot’s equations, the solutions are expressed by the Lippman-Schwinger integral equations, which can express the displacement and pressure fields. We derive the contrast-source integral equations of the decoupled poroelastic wave equations. We apply a conjugate-gradient fast Fourier transform method for fast solutions of the integral equations. We show that despite the complexity of the geologic structure, the numerical method enables the modeling of the displacement and pressure fields in the frequency and time domains. We determine that the wave scattering problem for the Biot model provides a good description to understand the earth’s interior.

Nonlinear Dynamics Research of Ground Undulatory Fin Robot with Flexible Deformation and Frictional Contact.

The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

Marine Radar Constant False Alarm Rate Detection in Generalized Extreme Value Distribution Based on Space-Time Adaptive Filtering Clutter Statistical Analysis

The performance of marine radar constant false alarm rate (CFAR) detection method is significantly influenced by the modeling of sea clutter distribution and detector decision rules. The false alarm rate and detection rate are therefore unstable. In order to address low CFAR detection performance and the modeling problem of non-uniform, non-Gaussian, and non-stationary sea clutter distribution in marine radar images, in this paper, a CFAR detection method in generalized extreme value distribution modeling based on marine radar space-time filtering background clutter is proposed. Initially, three-dimensional (3D) frequency wave-number (space-time) domain adaptive filter is employed to filter the original radar image, so as to obtain uniform and stable background clutter. Subsequently, generalized extreme value (GEV) distribution is introduced to integrally model the filtered background clutter. Finally, Inclusion/Exclusion (IE) with the best performance under the GEV distribution is selected as the clutter range profile CFAR (CRP-CFAR) detector decision rule in the final detection. The proposed method is verified by utilizing real marine radar image data. The results indicate that when the Pfa is set at 0.0001, the proposed method exhibits an average improvement in PD of 2.3% compared to STAF-RCBD-CFAR, and a 6.2% improvement compared to STCS-WL-CFAR. When the Pfa is set at 0.001, the proposed method exhibits an average improvement in PD of 6.9% compared to STAF-RCBD-CFAR, and a 9.6% improvement compared to STCS-WL-CFAR.

Mathematical model for constructing a matrix of coefficients thermal conductivity under low-temperature influence on the multilayer epidermis of biological tissue

Objective. The purpose of the study is to develop a mathematical model for constructing a matrix of thermal conductivity coefficients under low-temperature exposure to the multilayer epidermis of biological tissue. Method. The research is based on methods of thermo dynamic analysis, full-scale and computational modeling of processes under low-temperature influence. Result. A mathematical model of the matrix of thermal conductivity coefficients under low-temperature effects on biological tissue has been developed. Heat transfer in a multilayer medium under low-temperature influence on biological tissue is presented as a process with a discrete step in time and coordinate. Thermal properties are evenly distributed throughout the volume of layers of biological tissue. For exposure to cold, layers of the epidermis of biological tissue were used, divided into uniform identical cells, where the cell area of the biological tissue was taken to be equal to one. Conclusion. The results obtained in this work can be useful to specialists who deal with modeling problems with free boundaries.