Explicit Mathematical Expressions Research Articles

Outage performance of users in CR-NOMA network systems

<p>Non-Orthogonal Multiple Access (NOMA) and Cognitive Radio (CR) technologies present viable solutions to mitigate spectrum scarcity in wireless communication systems. This paper focuses on evaluating the performance of CR-NOMA networks, particularly for user devices operating under a Simultaneous Wireless Information and Power Transfer (SWIPT) framework. We derive explicit mathematical expressions for key performance metrics, including outage probability (OP) and system throughput, as they relate to various power allocation coefficients. Comprehensive simulations are conducted to validate our theoretical findings, revealing that appropriate power allocation significantly impacts user fairness and overall network throughput. The analysis covers a wide range of realistic channel conditions, including Rayleigh fading, to ensure robustness. Additionally, our study addresses the challenge of limiting interference to the primary network by optimizing the transmission power of secondary users while adhering to interference constraints. The results show that the primary user device (D<sub>1</sub>) consistently outperforms the secondary user device (D<sub>2</sub>), emphasizing the importance of strategic resource management. These contributions provide deeper insights into the factors affecting outage performance in CR-NOMA systems, offering effective solutions for enhancing the robustness, fairness, and efficiency of next-generation wireless communication networks.</p>

New charged anisotropic solution in f(Q)-gravity and effect of non-metricity and electric charge parameters on constraining maximum mass of self-gravitating objects

In the present article, A new class of singularity-free charged anisotropic stars is derived in f(Q)-gravity regime. To solve the field equations, we assume a particular form of anisotropy along with an electric field and obtain a new exact solution in f(Q)-gravity. The explicit mathematical expression for the model parameters is derived by the smooth joining of the obtained solutions with the exterior Reissner–Nordstrom de-Sitter solution across the bounding surface of a compact star along with the requirement that the radial pressure vanishes at the boundary. We have modeled four self-gravitating pulsar objects such as LMC X-4, PSR J1903+327, PSR J1614-2230, and GW190814 in our current study and predict the radii of these objects that fall between 8 and 10 km. Furthermore, the physical validity of the solution is performed for self-gravitating object PSR J1614-2230 with mass 1.97±0.04M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.97\\pm 0.04~M_{\\odot }$$\\end{document} with radius 10 km. The solution successfully fulfills all the physical requirements along with the stability and hydrostatic equilibrium conditions for a well-behaved model. The non-metricity f(Q)-parameter χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}$$\\end{document} and electric charge parameter η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} play an important role in the maximum mass of the objects. The maximum mass increases when χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}$$\\end{document} and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} increase but a non-collapsing stable object can be obtained when χ1≤0.0205\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{_1}\\le 0.0205$$\\end{document} and η≤0.0006\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\le 0.0006$$\\end{document}.

Sound diffraction by knife-edges of finite length: Integral solution, dimensionless parameters, and explicit formulas.

Sound diffraction by knife-edges of finite length is considered in the frequency domain. An approximate analytical solution in integral form is derived from a previously published time domain solution. Unlike the well-established finite length diffraction solution by Svensson et al. [Acta Acust. Acust. 95(3) 568-572 (2009)], the presented solution contains no singularities and both solutions agree, except very close to the diffracting edge. It is shown that finite length diffraction can be studied based on two dimensionless parameters: one expressing the receiver's proximity to the shadow boundary and one associated with the edge length. Depending on the dimensionless parameters, a given edge can be considered a short edge, an infinitely long edge or an edge of medium length, each case with different characteristics. Furthermore, a nomograph and the corresponding database are presented. They provide the normalized diffracted field for any source/receiver location, any source frequency, and any edge length. Also, easy to compute explicit mathematical expressions are presented to approximate the analytical integral solution. These expressions, along with the database method, accelerate diffraction calculations by order of magnitude compared to the presented integral solution or the Svensson solution. Finally, predictions from all proposed methods agree reasonably well with experimental data.

Graphene-based phononic crystal lenses: Machine learning-assisted analysis and design

The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing.

Carbon-footprint based concrete proportion design using LSTM and MOPSO algorithms

Artificial intelligence can design more sustainable concrete mixtures to reduce costs and CO2 emissions. In this paper, a concrete mix ratio design method based on deep learning algorithm and meta-heuristic algorithm is proposed. The main parameters that control and affect the strength of the concrete were selected as input variables, including Cement, Fly ash, Blast furnace slag, Water, Superplasticizer, Coarse aggregate, and Fine aggregate of concrete per unit volume. The compressive strength of concrete as output variables, a long short-term memory network model was developed to predict and explain the compressive strength characteristics of concrete. Sensitivity analysis showed that cementitious material and concrete age are the most important factors affecting the compressive strength of concrete. This is in good agreement with the relevant theoretical research. Taking the trained prediction model as the objective function of compressive strength of concrete mix ratio design, combined with the concrete material cost and carbon emission from cradle to gate, the multi-objective particle swarm optimization algorithm is used to optimize the proportion of each component of concrete to find the optimal mix ratio under specific conditions. The results show that the long short-term memory network can predict the compressive strength of concrete with high accuracy, and replace the traditional explicit mathematical expression to simulate the complex nonlinear relationship of multiple parameters. The established algorithm can calculate the Pareto optimal solution set according to the objective function, and obtain the optimal mix ratio with the least material cost and carbon footprint while meeting the compressive strength required by the project. The results of this work provide an intelligent and efficient design method for determining concrete mix ratio design, which can provide a reference for practical engineering applications to a certain extent.

Innovative Insights on the Thin Square Plate Large Deflection Problem.

Thin plates subjected to transverse load and undergoing large deflections have been widely studied and published in the literature. However, there is still a lack of information and understanding about the membrane stresses created under large deflections and their associated Airy stress function, as displayed in the well-known von Kármán equations set. The present study aims at providing explicit expressions for the membrane stresses, the deflections, and the Airy stress function for a general square plate area vertically uniformly loaded to reach large deflection state. This was obtained by using the results of a high-fidelity finite element analysis applied on a lateral loaded simply supported thin square plate, which are then casted to yield approximate Fourier series expressions for the membrane stresses, deflections, and the Airy stress function. The stress map figures provide a good understanding of the critical points on the plate, while the explicit mathematical expressions enabled the calculation of deflections and stresses for the entire plate area. Among other interesting findings, the presence of relatively high tensile and compressive membrane stresses existing near the plate edges was revealed, which might lead to potential failure hazards. The derivatives of the deflections and the Airy stress function enabled the validation of the large deflections von Kármán equations set for the investigated case, and it turned out that the generated expressions for the stresses and the lateral deflection based on a high-fidelity finite element model satisfy the second equation with a good accuracy, while the first one remains to further be investigated. Moreover, using the generated explicit equations, the load influence on the deflections and stresses was also analyzed to yield general novel expressions for the medium and very large deflections states. To generalize the investigated case, the stresses and the deflections were non-dimensionalized so they can be used for any material and plate dimensions.

Modelling of Viscosity and Thermal Conductivity of Water-Based Nanofluids using Machine-Learning Techniques

In this study, a variety of machine-learning algorithms are used to predict the viscosity and thermal conductivity of several water-based nanofluids. Machine learning algorithms, namely decision tree, random forest, extra tree, KNN, and polynomial regression, have been used, and their performances have been compared. The input parameters for the prediction of the thermal conductivity of nanofluids include temperature, concentration, and the thermal conductivity of nanoparticles. A three-input and a two-input model were utilized in modelling the viscosity of nanofluid. Both models considered temperature and concentration as input parameters, and additionally, the type of nanoparticle was considered for the three-input model. The order of importance of the most influential parameters in predicting both viscosity and thermal conductivity was studied. A wider range of input parameters have been considered in an open-access database. With the existing experimental data, all of the developed machine learning models exhibit reasonable agreement. Extra trees were found to provide the best results for estimating thermal conductivity, with a value of 0.9403. In predicting viscosity using a three-input model, extra trees were found to provide the best result with a value of 0.9771, and decision trees were found to provide the best results for estimating the viscosity using a two-input model with a value of 0.9678. In order to study heat transport phenomena through mathematical modelling, it is important to have an explicit mathematical expression. Therefore, the formulation of mathematical expressions for predicting viscosity and thermal conductivity has been carried out. Additionally, a comparison with the Xue and Maxwell thermal conductivity models is made to validate the results of this study, and the results are observed to be reliable.

A Theoretical Approach to the Complex Chemical Evolution of Phosphorus in the Interstellar Medium

The study of phosphorus chemistry in the interstellar medium has become a topic of growing interest in astrobiology because it is plausible that a wide range of P-bearing molecules were introduced in the early Earth by the impact of asteroids and comets on its surface, enriching prebiotic chemistry. Thanks to extensive searches in recent years, it has become clear that P mainly appears in the form of PO and PN in molecular clouds and star-forming regions. Interestingly, PO is systematically more abundant than PN by factors typically of ∼1.4–3, independently of the physical properties of the observed source. In order to unveil the formation routes of PO and PN, in this work we introduce a mathematical model for the time evolution of the chemistry of P in an interstellar molecular cloud and analyze its associated chemical network as a complex dynamical system. By making reasonable assumptions, we reduce the network to obtain explicit mathematical expressions that describe the abundance evolution of P-bearing species and study the dependences of the abundance of PO and PN on the system’s kinetic parameters with much faster computation times than available numerical methods. As a result, our model reveals that the formation of PO and PN is governed by just a few critical reactions, and fully explains the relationship between PO and PN abundances throughout the evolution of molecular clouds. Finally, the application of Bayesian methods constrains the real values of the most influential reaction rate coefficients making use of available observational data.

How good can a simple artificial neural network predict the medium reorganization energy and the free energy gap from a steady-state fluorescence spectrum?

Medium reorganization energy, Erm, and free energy gap, ΔG, are key characteristics in determining the photoinduced charge transfer rate. They are strongly related to the width and position of the steady-state fluorescence and absorption spectra of organic dyes in solvents. Steady-state spectroscopy is one of the most standard techniques for studying organic dyes. Here, we present a simple machine learning model for cost-effective prediction the medium reorganization energy and the free energy gap from the steady-state fluorescence spectra. Fluorescence spectra with corresponding reference values of physical quantities are calculated using an explicit mathematical expression that addresses electronic-vibrational transitions, intramolecular and solvent reorganizations. An approach to the separate formation of data sets for training and validation is proposed. Gaussian noise is used in training to improve predictions. This study shows that Erm and ΔG can be predicted with the mean absolute error ∼0.024 eV and ∼0.009 eV, respectively. Robustness testing is performed on the experimental spectra of coumarin-153, coumarin-307, and coumarin-522B in a series of solvents.

A comparative study of black-box and white-box data-driven methods to predict landfill leachate permeability.

Due to the dynamic and complexity of leachate percolation within municipal solid waste (MSW), planning and operation of solid waste management systems are challenging for decision-makers. In this regard, data-driven methods can be considered robust approaches to modeling this problem. In this paper, three black-box data-driven models, including artificial neural networks (ANN), adaptive neuro-fuzzy inference systems (ANFIS), and support vector regression (SVR), and also three white-box data-driven models, including the M5 model tree (M5MT), classification and regression trees (CART), and group method of data handling (GMDH), were developed for modeling and predicting landfill leachate permeability ([Formula: see text]). Based on a previous study conducted by Ghasemi et al. (2021), [Formula: see text] can be formulated as a function of impermeable sheets ([Formula: see text]) and copper pipes ([Formula: see text]). Hence, in the present study, [Formula: see text] and [Formula: see text] were adopted as input variables for the prediction of [Formula: see text] and evaluated for the performance of the suggested black-box and white-box data-driven models. Scatter plots and statistical indices such as coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE) were used for qualitative and quantitative evaluations of the effectiveness of the suggested methods. The outcomes indicated all of the provided models successfully predicted [Formula: see text]. However, ANN and GMDH had higher accuracy between the proposed black-box and white-box data-driven models. ANN with R2 = 0.939, RMSE = 0.056, and MAE = 0.017 was marginally better than GMDH with R2 = 0.857, RMSE = 0.064, and MAE = 0.026 in the testing stage. Nevertheless, an explicit mathematical expression provided by GMDH to predict k was easier and more understandable than ANN.

Eccentricity design for the coolant distribution optimization of a practical commercial-size proton exchange membrane fuel cell stack using a novel proper orthogonal decomposition based analysis model

The uniform distribution of coolant among different coolant flow field plates is of critical importance to the thermal management of proton exchange membrane fuel cell (PEMFC) stacks. Herein, the coolant distribution uniformity is optimized using an eccentric end socket structure based on the computational fluid dynamic (CFD) method. Firstly, the grid systems are comprehensively tested for the refined simulation requirements under a well-distributed condition and a high current density. Then, to reduce the heavy burden of computing resources, a novel analysis model is proposed to further establish the explicit mathematical expression between the coolant distribution curve (CDC) and the eccentricity based on the CFD results and proper orthogonal decomposition (POD). Finally, the coolant distribution uniformity is optimized according to the above explicit expression. Results suggest that for the studied cases, the grid systems with the manifold cross section grid numbers take 4 480 and 8 385 can be regarded as the grid-independent ones under the eccentricity ranges of 0 ∼ 0.7 and 0.7 ∼ 1.0 respectively. The simulated stack pressure drops show a high consistence with the experimental ones with a maximum relative deviation of 10%, validating the reliability of the CFD model. With the increase of the eccentricity, the coolant distribution non-uniformity decreases firstly and finally increase. The CDCs are similar if the eccentricity vector points to the same side of the transverse eccentricity axis. The optimized coolant distribution non-uniformity (1.58%) reduces 4.04 times compared with that in the benchmark case (6.38%) when the eccentricity takes 0.8856.

Preset model of bending force in 6-high universal crown tandem cold rolling mill based on symbolic regression

ABSTRACT Highly accurate bending force presetting is a prerequisite to ensure the well flatness of the strip head, however, there are limitations in the preset model used in industrial sites. According to the flatness control characteristics of work roll and intermediate roll bending forces, this paper integrates the historical production data of a 1420 mm 6-high tandem cold rolling mill and establishes a chain model of bending force preset based on symbolic regression, which implements with age-layered population structure genetic programming (ALPS-GPSR). The advantage of symbolic regression models is the ability to obtain explicit mathematical expressions, which is very important in complex industrial production environments. With the application of ALPS-GPSR based bending force preset model in the industrial site, the hit rate of flatness within 6IU in the strip head for three specifications of the strip has increased by 2.86%, 1.61%, and 2.19% respectively on average, achieving a satisfactory result.

Variance effective population size is affected by census size in sub-structured populations.

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (Ne ), and this 'temporal method' provides estimates of Ne referred to as variance effective size (NeV ). We show that NeV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (Nc ). The realized NeV of a local population can either increase or decrease with increasing m, depending on the relationship between Ne and Nc in isolation. This is shown by explicit mathematical expressions for the factors affecting NeV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of Nc on the realized NeV of a local subpopulation is most pronounced at high migration rates. We show that Nc only affects local NeV , whereas NeV for the metapopulation as a whole, inbreeding (NeI ), and linkage disequilibrium (NeLD ) effective size are all independent of Nc . Our results provide a possible explanation to the large variation of Ne /Nc ratios reported in the literature, where Ne is frequently estimated by NeV . They are also important for the interpretation of empirical Ne estimates in genetic management where local NeV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation NeV as a proxy for NeI .

The Varying Earth’s Radiative Feedback Connected to the Ocean Energy Uptake: A Theoretical Perspective from Conceptual Frameworks

Abstract When quadrupling the atmospheric CO2 concentration in relation to preindustrial levels, most global climate models show an initially strong net radiative feedback that significantly reduces the energy imbalance during the first two decades after the quadrupling. Afterward, the net radiative feedback weakens, needing more surface warming than before to reduce the remaining energy imbalance. Such weakening radiative feedback has its origin in the tropical oceanic stratiform cloud cover, linked to an evolving spatial warming pattern. In the classic linearized energy balance framework, such variation is represented by an additional term in the planetary budget equation. This additional term is usually interpreted as an ad hoc emulation of the cloud feedback change, leaving unexplained the relationship between this term and the spatial warming pattern. I use a simple nonlinearized energy balance framework to justify that there is a physical interpretation of this term: the evolution of the spatial pattern of warming is explained by changes in the ocean’s circulation and energy uptake. Therefore, the global effective thermal capacity of the system also changes, leading to the additional term. In reality, the clouds respond to what occurs in the ocean, changing their radiative effect. In the equation, the term is now a concrete representation of the ocean’s role. Additionally, I derive for the first time an explicit mathematical expression of the net radiative feedback and its temporal evolution in the linearized energy balance framework. This mathematical expression supports the new proposed interpretation. As a corollary, it justifies the 20-yr time scale used to study the variation of the net radiative feedback. Significance Statement Linearized energy balance models have helped the study of Earth’s radiative response. However, the present linear models are at the edge of usefulness to get more insights. In this work, I justify that part of the nonlinearity in the radiative response can be explained without peculiar atmospheric radiative feedback mechanisms or a nonlinearity in the radiative response. Instead, the concept of an evolving thermal capacity recovers the ocean’s role in redistributing the energy, changing the spatial warming pattern, and, finally, altering the atmospheric feedback mechanisms. This work also justifies the time scales used in the field for studying the variation of the net radiative feedback.

A near‐optimal CUSUM‐CV chart

AbstractMonitoring of the process coefficient of variation (CV) with one‐sided CUSUM charts has been considered in the literature. In this short note, we develop a near‐optimal one‐sided CUSUM chart (with an explicit mathematical expression of the reference parameter) for detecting either increases or decreases in the CV of a normally distributed process. It is shown that the run‐length profiles of the existing and proposed one‐sided CUSUM‐CV charts (despite the fact that both charts possess different control‐charting structures) approximately remain the same. However, the proposed one‐sided CUSUM‐CV charts can be easily optimized when detecting a specific upward or downward shift in the in‐control process CV.

Delay-Oriented Scheduling in 5G Downlink Wireless Networks Based on Reinforcement Learning With Partial Observations

5G wireless networks are expected to satisfy different delay requirements of various traffics by network resource scheduling. Existing scheduling methods perform poorly in practice due to their unrealistic assumption on the access to the full channel state information (CSI) or the explicit mathematical expression of network delay. In this paper, we consider the delay-oriented packet scheduling problem in multi-cell 5G downlink networks with multiple users and traffic types (e.g., FTP, VoIP and video streaming), and formulate it as a partially observable Markov decision process (POMDP). We design a delay-oriented downlink scheduling framework based on deep reinforcement learning (DRL) to autonomously schedule the active traffic flows without the full channel information. Furthermore, a recurrent proximal policy optimization (RPPO) algorithm is proposed to perceive the underlying state and accelerate learning under different time granularities, with the policy gradient theorem under POMDP strictly proved. By incorporating the future traffic information provided by a proposed spatial-temporal prediction algorithm, RPPO can balance the load and achieve lower delay in real-time multi-cell multi-user scenarios. Results of extensive experiments on a realistic 5G simulator demonstrate that our framework significantly outperforms existing approaches in terms of both tail delay and average delay for up to 48% and 41.7%, respectively.

An improved Fractional MPPT Method by Using a Small Circle Approximation of the P–V Characteristic Curve

This paper presents an analytical solution to the maximum power point tracking (MPPT) problem for photovoltaic (PV) applications in the form of an improved fractional method. The proposal makes use of a mathematical function that describes the relationship between power and voltage in a PV module in a neighborhood including the maximum power point (MPP). The function is generated by using only three points of the P–V curve. Next, by using geometrical relationships, an analytical value for the MPP can be obtained. The advantage of the proposed technique is that it provides an explicit mathematical expression for calculation of the voltage at the maximum power point (vMPP) with high accuracy. Even more, complex calculations, manufacturer data, the measurements of short circuit current (iSC) and open-circuit voltage (vOC) are not required, making the proposal less invasive than other solutions. The proposed method is validated using the P–V curve of one PV module. Experimental work demonstrates the speed in the calculation of vMPP and the feasibility of the proposed solution. In addition, this MPPT proposal requires only the typical and available measurements, namely, PV voltage and current. Consequently, the proposed method could be implemented in most PV applications.

Gene Expression Programming (GEP) Modelling of Sustainable Building Materials including Mineral Admixtures for Novel Solutions

In this study, the employment of the gene expression programming (GEP) technique in forecasting models on sustainable construction materials including mineral admixtures and civil engineering quantities (e.g., compressive strength), was investigated. Compared to the artificial neural networks (ANN) based formulations, which are often too complicated to be used, GEP-based derived models provide estimation equations that are reasonably simple and may be used for practical design purposes and even for hand calculations. Many popular models, such as best-fitted curves based on regression analyses, multi-linear regression (MLR), multinomial logistic regression (MNLR), and multinomial variate regression (MNVR), can also be used for construction materials properties modeling. However, due to the nonlinearity and complexity of the target properties, the models established using linear regression analyses may not reveal the precise behavior. Additionally, regression models lack generality, and this comes from the fact that some functions are defined for regression in classical regression techniques; while in the GEP approach, there is no predefined function to be considered, and it reproduces or omits various combinations of parameters to provide the formulation that fits the experimental outcomes. If the input parameters can be evaluated through simple laboratory or rapid measurements, and also a comprehensive experimental database is made available, the models can be constructed with optimal flexibility. Flexibility in choosing the complexity and fitness functions, such as RMSE, MAE, and MSE, might lead to better performance of the approach and well-capturing the governing pattern behind the material’s characteristics. There may be minor inaccuracies with this technique; however, the explicit mathematical expressions, which can be easily implemented in the design and analysis process, may cover the minor inaccuracies compared to ANN, support vector machine (SVM), and other intelligent approaches. Based on the presented study, sometimes it would be better to provide more than one GEP model and consider different combinations of input contributing variables to afford the possible initial feed for a more settled and comprehensive model. Mostly, GEP’s strengths as a superior machine learning technique in modeling the behavior of construction materials including mineral admixtures, leading to innovative solutions in civil engineering, have been presented.

Field-view theoretical model of triboelectric nanogenerators based on Laplace's equations

Further investigation of theoretical models is essential to physically understand triboelectric nanogenerators (TENGs) and then promote their extensive applications. Theoretical approaches in the existing studies mainly focus on establishing equivalent circuits, which provide a rapid analysis method but with relatively low precision. Therefore, we propose a field-view model to theoretically analyze the physical mechanism of TENGs, which reveals high efficiency and great accuracy. After the comprehensive study, it is determined that the dynamic behavior of TENGs in a single approaching/separating cycle could be regarded as a time series of electrostatic equilibrium problems. Thus, based on Laplace's equations and potential boundary conditions, a definite-solution-problem model is developed, which could provide explicit mathematical expressions to ultra-precisely predict the electrical characteristics of TENG.

Improving Symbolic Regression for Predicting Materials Properties with Iterative Variable Selection.

Symbolic regression offers a promising avenue for describing the structure-property relationships of materials with explicit mathematical expressions, yet it meets challenges when the key variables are unclear because of the high complexity of the problems. In this work, we propose to solve the difficulty by automatically searching for important variables from a large pool of input features. A new algorithm that integrates symbolic regression with iterative variable selection (VS) was designed for optimization of the model with a large amount of input features. Using the recent method SISSO for symbolic regression and random search for variable selection, we show that the VS-assisted SISSO (VS-SISSO) can effectively manage even hundreds of input features that the SISSO alone was computationally hindered, and it fastly converges to (near) optimal solutions when the model complexity is not high. The efficiency of this approach for improving the accuracy of symbolic regression in materials science was demonstrated in the two showcase applications of learning approximate equations for the band gap of inorganic halide perovskites and the stability of single-atom alloy catalysts.