Symbolic Regression Models Research Articles

Circular rubber aggregate CFST stub columns under axial compression: prediction and reliability analysis

Extensive studies support using steel tubes to enhance the structural integrity of rubber aggregate concrete (RBAC), namely RBAC-filled steel tubes (RCFST). However, current design codes for assessing the axial compressive behaviour of circular stub RCFST (CS-RCFST) columns are limited. Furthermore, there is a scarcity of studies focused on ensuring the structural safety of these columns. Based on an extensive experimental database comprising 145 columns, this study explores machine learning (ML) capabilities for predicting the axial strength of CS-RCFST columns, using six typical machine-learning models, i.e., symbolic regression (SR), XGBoost, CatBoost, random forest, LightGBM, and Gaussian process regression models. The hyperparameter tuning of the introduced ML models is performed using the Bayesian Optimization technique. The comparison results show that the CatBoost model is the most reliable and accurate ML model (R2 = 0.999 and 0.993 for the training and testing sets, respectively). In addition, a simple and practical design expression for CS-RCFST columns has been developed with acceptable accuracy based on the SR model (an average test-to-prediction ratio of 0.99 and CoV of 0.132). Meanwhile, the axial strength predicted by ML models was compared with two prominent practice codes (i.e., AISC360 and EC4). The comparison results indicated that the ML models could introduce a highly reliable and accurate approach over current design standards for strength prediction. Furthermore, a reliability analysis is conducted on two different ML models to evaluate the reliability of utilising ML models in practical design applications. This assessment involves identifying the statistical properties associated with the compressive strength of RBAC, as well as introducing the required resistance design factors aligned with the target reliability recommended by code standards.

Modeling of the metal–insulator transition temperature in alio-valently doped VO2 through symbolic regression

The correlated semiconductor vanadium dioxide (VO2) exhibits an insulator–metal transition (IMT) near room temperature, which is of interest in various device applications. Precise IMT temperature control is crucial to determine the use cases across technologies such as thermochromic windows, actuators for robots or neuronal oscillators. Doping the cation or anion sites can modulate the IMT by several tens of degrees and control hysteresis. However, modeling the effects of control parameters (e.g., doping concentration, type of dopants) is challenging due to complex experimental procedures and limited data, hindering the use of traditional data-driven machine learning approaches. Symbolic regression (SR) can bridge this gap by identifying nonlinear expressions connecting key input parameters to target properties, even with small data sets. In this work, we develop SR models to capture the IMT trends in VO2 influenced by different dopant parameters. Using experimental data from the literature, our study reveals a dual nature of the IMT temperature with varying tungsten (W) doping concentrations. The symbolic model captures data trends and accounts for experimental variability, providing a complementary approach to first-principles calculations. Our feature-driven analysis across a broader class of dopants informs selectivity and provides qualitative insights into tuning phase transition properties valuable for neuromorphic computing and thermochromic windows.

Predicting the compressive strength of recycled aggregate concrete using machine learning models

This paper investigates the compressive strength of recycled aggregate concrete (RAC) using machine learning models, specifically the Symbolic Regression (SR) and XGBoost models. The dataset consists of 1,047 experimental samples collected from 40 published studies, allowing for accurate prediction of compressive strength based on parameters such as cement content, water, fine aggregates, and recycled aggregates. The results show that the XGBoost model achieved high accuracy with an MAE of 4.65 MPa and an RMSE of 7.61 MPa. The paper also analyzes the influence of these parameters on compressive strength using the SHAP method, emphasizing the importance of understanding the correlations between variables to optimize recycled concrete design.

Good results from sensor data: Performance of machine learning algorithms for regression problems in chemical sensors

Accurately predicting unseen data, instead of mere memorization of training examples, is a critical goal of machine learning. This generalization is particularly important in the field of chemical sensors, where the ability to accurately predict the chemical properties or concentration levels of unknown samples is crucial. The paper presents a comprehensive yet accessible introduction to various machine learning concepts, highlighting the importance of model interpretability and generalization in ensuring reliable and accurate results in this context. Nonlinear sensor array data are utilized to introduce key concepts (e.g., bias-variance tradeoff) and techniques (linear models, partial least squares regression, support vector machines, k-nearest neighbors, decision trees, ensemble methods, automated machine learning, symbolic regression, and artificial neural networks), providing a solid foundation to make informed decisions when selecting machine learning techniques for sensor-specific regression applications. The results clearly indicate a number of conclusions. First, overparameterized deep feedforward neural networks show great accuracy and generalization when trained on a sufficiently large dataset. Second, symbolic regression models proved to be more accurate than deep feedforward neural networks and classical machine learning techniques on smaller datasets. Third, the performance of various machine learning models was dataset-dependent, showing the importance of comparative studies to determine the most suitable approach. It is clear that the optimal model cannot be known a priori. This paper aims to provide a starting point for investigations on the performance of different machine learning techniques in chemical sensor applications.

Prediction and reliability analysis of shear strength of RC deep beams

This study explores machine learning (ML) capabilities for predicting the shear strength of reinforced concrete deep beams (RCDBs). For this purpose, eight typical machine-learning models, i.e., symbolic regression (SR), XGBoost (XGB), CatBoost (CATB), random forest (RF), LightGBM, support vector regression (SVR), artificial neural networks (ANN), and Gaussian process regression (GPR) models, are selected and compared based on a database of 840 samples with 14 input features. The hyperparameter tuning of the introduced ML models is performed using the Bayesian optimization (BO) technique. The comparison results show that the CatBoost model is the most reliable and accurate ML model (R2 = 0.997 and 0.947 in the training and testing sets, respectively). In addition, simple and practical design expressions for RCDBs have been proposed based on the SR model with a physical meaning and acceptable accuracy (an average prediction-to-test ratio of 0.935 and a standard deviation of 0.198). Meanwhile, the shear strength predicted by ML models was then compared with classical mechanics-driven shear models, including two prominent practice codes (i.e., ACI318, EC2) and two previous mechanical models, which indicated that the ML approach is highly reliable and accurate over conventional methods. In addition, a reliability-based design was conducted on two ML models, and their reliability results were compared with those of two code standards. The findings revealed that the ML models demonstrate higher reliability compared to code standards.

Li-ion battery state of health prediction through metaheuristic algorithms and genetic programming

Predicting the State of Health (SOH) of the Lithium-ion battery with higher accuracy and reduced cost is a challenging and crucial task for ensuring its reliability and safety. To achieve this, a two-stage prediction framework is proposed to find a concise expression of SOH using the health features of the battery through metaheuristic algorithms and genetic programming (GP).In Stage-I, three conflicting objectives are considered concurrently: the root-mean-square error (RMSE) of SOH prediction, the health features selected, and the expressional complexity of the battery capacity. The wrapper structure is utilized for SOH prediction, where a binary multi-objective grey wolf optimization (Binary MOGWO) algorithm is employed to select features and generate the Pareto set. Genetic programming is used to calculate the SOH value using symbolic regression models. In Stage-II, the final compromise solution is filtered from the Pareto set through decision-making approaches. The relationships between selected features and the capacity of the battery are investigated. The NASA Prognostics Center of Excellence battery dataset is chosen to verify the effectiveness of the proposed framework. The simulation results show that the features found through the framework can provide SOH predictions in the form of symbolic equations with higher accuracy, lower cost, and reduced complexity.

Predicting the Curie temperature of Sm-Co-based alloys via data-driven strategy

Calculating the Curie temperature of rare-earth permanent magnetic materials has remained a big theoretical challenge. In this study, based on a home-built Sm-Co-based alloys database, a data-driven machine learning approach was developed to predict the Curie temperature of Sm-Co-based alloys. High-throughput predictions of Curie temperature were achieved using a genetic program based symbolic regression model. A classification model based on logistic regression was established to quantify the effect of doping on the Curie temperature of Sm-Co-based alloys. The key physical descriptor affecting Curie temperature was extracted from the established machine learning models, and the Curie temperature sensitivity coefficient was defined. It was discovered that the doping elements with large electrical conductivity and similar heat of fusion to that of Sm are likely to increase the Curie temperature of Sm-Co-based alloys. The model predictions were verified quantitatively by the experimental results of a series of prepared Sm-Co-based samples. This work provides a high-efficiency method for developing Sm-Co-based permanent magnets with high Curie temperatures.

Individual chaotic behaviour of the S-stars in the Galactic centre

Located at the core of the Galactic centre, the S-star cluster serves as a remarkable illustration of chaos in dynamical systems. The long-term chaotic behaviour of this system can be studied with gravitational N-body simulations. By applying a small perturbation to the initial position of star S5, we can compare the evolution of this system to its unperturbed evolution. This results in two solutions that diverge exponentially, defined by the separation in position space δr, with an average Lyapunov timescale of ∼420 yr, corresponding to the largest positive Lyapunov exponent. Even though the general trend of the chaotic evolution is governed in part by the supermassive black hole Sagittarius A∗ (Sgr A∗), individual differences between the stars can be noted in the behaviour of their phase-space curves. We present an analysis of the individual behaviour of the stars in this Newtonian chaotic dynamical system. The individuality of their behaviour is evident from offsets in the position space separation curves of the S-stars and the black hole. We propose that the offsets originate from the initial orbital elements of the S-stars, where Sgr A∗ is considered in one of the focal points of the Keplerian orbits. Methods were considered to find a relation between these elements and the separation in position space. Symbolic regression provides the clearest diagnostics for finding an interpretable expression for the problem. Our symbolic regression model indicates that ⟨δr⟩ ∝ e2.3, implying that the time-averaged individual separation in position space increases rapidly with the initial eccentricity of the S-stars.

Empirical Turbulence Interaction Noise Model for Permeable Flat Plate Leading Edges

One of the major aerodynamic noise generation mechanisms is the interaction of a turbulent flow with a downstream blunt object, such as the blade of a rotating fan or a fixed stator. A possible method to reduce this noise is the use of flow-permeable leading edges, which has been investigated experimentally on a set of flat plates with different leading-edge perforations. The results show that these modifications can lead to notable noise reductions at low and medium frequencies, but also to a noise increase at high frequencies due to the contribution of surface roughness noise. The measured data were then used as an input to a symbolic regression modeling approach with the aim of obtaining a simple yet accurate model to predict the noise reduction capacity of the permeable leading edges. Three different prediction models were finally selected to demonstrate the capability of the current approach. One of the more complex models already predicts correct trends and shows an acceptable mean absolute error, making it a reliable candidate for engineering purposes.

An Analysis of the Ingredients for Learning Interpretable Symbolic Regression Models with Human-in-the-loop and Genetic Programming

Interpretability is a critical aspect to ensure a fair and responsible use of machine learning (ML) in high-stakes applications. Genetic programming (GP) has been used to obtain interpretable ML models because it operates at the level of functional building blocks: if these building blocks are interpretable, there is a chance that their composition (i.e., the entire ML model) is also interpretable. However, the degree to which a model is interpretable depends on the observer. Motivated by this, we study a recently-introduced human-in-the-loop system that allows the user to steer GP’s generation process to their preferences, which shall be online-learned by an artificial neural network (ANN). We focus on the generation of ML models as analytical functions (i.e., symbolic regression) as this is a key problem in interpretable ML, and propose a two-fold contribution. First, we devise more general representations for the ML models for the ANN to learn upon, to enable the application of the system to a wider range of problems. Second, we delve into a deeper analysis of the system’s components. To this end, we propose an incremental experimental evaluation, aimed at (1) studying the effectiveness by which an ANN can capture the perceived interpretability for simulated users, (2) investigating how the GP’s outcome is affected across different simulated user feedback profiles, and (3) determining whether humans participants would prefer models that were generated with or without their involvement. Our results pose clarity on pros and cons of using a human-in-the-loop approach to discover interpretable ML models with GP.

Generalizability Improvement of Interpretable Symbolic Regression Models for Quantitative Structure-Activity Relationships.

In the pursuit of optimal quantitative structure-activity relationship (QSAR) models, two key factors are paramount: the robustness of predictive ability and the interpretability of the model. Symbolic regression (SR) searches for the mathematical expressions that explain a training data set. Thus, the models provided by SR are globally interpretable. We previously proposed an SR method that can generate interpretable expressions by humans. This study introduces an enhanced symbolic regression method, termed filter-induced genetic programming 2 (FIGP2), as an extension of our previously proposed SR method. FIGP2 is designed to improve the generalizability of SR models and to be applicable to data sets in which cost-intensive descriptors are employed. The FIGP2 method incorporates two major improvements: a modified domain filter to eradicate diverging expressions based on optimal calculation and the introduction of a stability metric to penalize expressions that would lead to overfitting. Our retrospective comparative analysis using 12 structure-activity relationship data sets revealed that FIGP2 surpassed the previously proposed SR method and conventional modeling methods, such as support vector regression and multivariate linear regression in terms of predictive performance. Generated mathematical expressions by FIGP2 were relatively simple and not divergent in the domain of function. Taken together, FIGP2 can be used for making interpretable regression models with predictive ability.

Prediction of the axial compression capacity of stub CFST columns using machine learning techniques.

Concrete-filled steel tubular (CFST) columns have extensive applications in structural engineering due to their exceptional load-bearing capability and ductility. However, existing design code standards often yield different design capacities for the same column properties, introducing uncertainty for engineering designers. Moreover, conventional regression analysis fails to accurately predict the intricate relationship between column properties and compressive strength. To address these issues, this study proposes the use of two machine learning (ML) models-Gaussian process regression (GPR) and symbolic regression (SR). These models accept a variety of input variables, encompassing geometric and material properties of stub CFST columns, to estimate their strength. An experimental database of 1316 specimens was compiled from various research papers, including circular, rectangular, and double-skin stub CFST columns. In addition, a dimensionless output variable, referred to as the strength index, is introduced to enhance model performance. To validate the efficiency of the introduced models, predictions from these models are compared with those from two established standard codes and various ML algorithms, including support vector regression optimized with particle swarm optimization (PSVR), artificial neural networks, XGBoost (XGB), CatBoost (CATB), Random Forest, and LightGBM models. Through performance metrics, the CATB, GPR, PSVR and XGB models emerge as the most accurate and reliable models from the evaluation results. In addition, simple and practical design equations for the different types of CFST columns have been proposed based on the SR model. The developed ML models and proposed equations can predict the compressive strength of stub CFST columns with reliable and accurate results, making them valuable tools for structural engineering. Furthermore, the Shapley additive interpretation (SHAP) technique is employed for feature analysis. The results of the feature analysis reveal that section slenderness ratio and concrete strength parameters negatively impact the compressive strength index.

The long and short of it: a comprehensive assessment of axial length estimation in myopic eyes from ocular and demographic variables.

Axial length, a key measurement in myopia management, is not accessible in many settings. We aimed to develop and assess machine learning models to estimate the axial length of young myopic eyes. Linear regression, symbolic regression, gradient boosting and multilayer perceptron models were developed using age, sex, cycloplegic spherical equivalent refraction (SER) and corneal curvature. Training data were from 8135 (28% myopic) children and adolescents from Ireland, Northern Ireland and China. Model performance was tested on an additional 300 myopic individuals using traditional metrics alongside the estimated axial length vs age relationship. Linear regression and receiver operator characteristics (ROC) curves were used for statistical analysis. The contribution of the effective crystalline lens power to error in axial length estimation was calculated to define the latter's physiological limits. Axial length estimation models were applicable across all testing regions (p ≥ 0.96 for training by testing region interaction). The linear regression model performed best based on agreement metrics (mean absolute error [MAE] = 0.31 mm, coefficient of repeatability = 0.79 mm) and a smooth, monotonic estimated axial length vs age relationship. This model was better at identifying high-risk eyes (axial length >98th centile) than SER alone (area under the curve 0.89 vs 0.79, respectively). Without knowing lens power, the calculated limits of axial length estimation were 0.30 mm for MAE and 0.75 mm for coefficient of repeatability. In myopic eyes, we demonstrated superior axial length estimation with a linear regression model utilising age, sex and refractive metrics and showed its clinical utility as a risk stratification tool.

High-cycle fatigue life prediction of L-PBF AlSi10Mg alloys: a domain knowledge-guided symbolic regression approach.

The large scatter in high-cycle fatigue (HCF) life poses significant challenges to safe and reliable in-service assessment of additively manufactured metal components. Previous investigations have indicated that inherent manufacturing defects are a critical factor affecting the fatigue performance of the components, and the HCF life is significantly influenced by the geometric parameters of the critical defects inducing crack nucleation. Therefore, it is highly important to elucidate the correlation of the HCF life with the geometric parameters of critical defects. This study proposes a new fatigue life prediction model for laser additively manufactured AlSi10Mg alloys by including the combined effects of loading stress and defect geometries (size, location and morphology) in terms of domain knowledge-guided symbolic regression (SR). Domain knowledge is extracted from the semi-empirical Murakami, Z-parameter and X-parameter fatigue life models to establish the variable subtrees. The results show that compared with these semi-empirical models, the domain knowledge integration-based SR model has higher prediction accuracy and generalization ability. Moreover, compared with traditional 'black box' machine learning models, SR excels at balancing prediction accuracy and model interpretability, which provides useful insights into the relationship between fatigue life and defect geometries. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Relating the combinatorial materials chip mapping to the glass-forming ability of bulk metallic glasses via diffraction peak width

There is a gap between the cooling rate of thin film deposition (∼108 K/s) and bulk metallic glass (BMG) casting (∼103 K/s). In this work, we tried to corelate the glass-forming range (GFR) determined from the combinatorial materials chip (CMC) with the glass-forming ability (GFA) of BMG. Data from five CMCs and the reported critical casting diameter (Dmax) of BMGs were used as the dataset. It is found that the full-width at half maximum (FWHM) of the first sharp diffraction peak (FSDP) is a good indicator of the GFA of BMG as suggested by Liu et al. [1]. Strong positive correlations between the FWHM and Dmax are shown in the Zr-, Ag-, Cu-, Fe-, La-, and Mg-based BMG systems. Furthermore, the Pearson correlation coefficients of the symbolic regression (SR) models indicate possible similarity in the GFA natures of the Ag-Zr, Cu-Zr, Cu-Ag, and Mg-La pairs.

Computation of flow rates in rarefied gas flow through circular tubes via machine learning techniques

Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates W used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius l∈[0,5]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l \\in [0,5]$$\\end{document} and downstream over upstream pressure p∈[0,0.9]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \\in [0,0.9]$$\\end{document}) in a very wide range of the gas rarefaction parameter δ∈[0,103]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\in [0,10^3]$$\\end{document}. The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than 12.5%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12.5\\%$$\\end{document}. Various expressions of the form of W=W(p,l,δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W=W(p,l,\\delta )$$\\end{document} with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than 17%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17\\%$$\\end{document}. To further improve the accuracy, the dataset is divided into three subsets in terms of δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document} and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than 9%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9\\%$$\\end{document}. Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.

Exploring interpretable features of hardness for intermetallic compounds prepared by spark plasma sintering

Intermetallic compounds, known for their excellent hardness, conductivity, and strength, have significant applications in aerospace and automotive industries. Hardness is a crucial mechanical property in the development and optimization of intermetallic compounds (IMCs), and meanwhile, spark plasma sintering (SPS) serves as a prevalent technique for preparing IMCs. In this study, a dataset of Vickers hardness of binary intermetallic compounds prepared by SPS and potential feature sets influencing the target performance (HV) were collected. Three machine-learning strategies were developed and comprehensively evaluated. The first strategy focuses on processing parameters and compositions, the second incorporates physical properties in addition to the features considered in the first strategy, and the third one employs a combined feature engineering based on the second strategy. The third strategy, which includes three screened features through a rigorous feature engineering process, achieves the highest predictive accuracy. Subsequently, a symbolic regression (SR) model based on genetic programming (GP) was employed to develop a physically interpretable formula linking the target performance with the selected features. The findings of this study are of significance for developing high-performance intermetallic compounds.

Revealing metastatic castration-resistant prostate cancer master regulator through lncRNAs-centered regulatory network.

Metastatic castration-resistant prostate cancer (mCRPC) is an aggressive form of cancer unresponsive to androgen deprivation therapy (ADT) that spreads quickly to other organs. Despite reduced androgen levels after ADT, mCRPC development and lethality continues to be conducted by the androgen receptor (AR) axis. The maintenance of AR signaling in mCRPC is a result of AR alterations, androgen intratumoral production, and the action of regulatory elements, such as noncoding RNAs (ncRNAs). ncRNAs are key elements in cancer signaling, acting in tumor growth, metabolic reprogramming, and tumor progression. In prostate cancer (PCa), the ncRNAs have been reported to be associated with AR expression, PCa proliferation, and castration resistance. In this study, we aimed to reconstruct the lncRNA-centered regulatory network of mCRPC and identify the lncRNAs which act as master regulators (MRs). We used publicly available RNA-sequencing to infer the regulatory network of lncRNAs in mCRPC. Five gene signatures were employed to conduct the master regulator analysis. Inferred MRs were then subjected to functional enrichment and symbolic regression modeling. The latter approach was applied to identify the lncRNAs with greater predictive capacity and potential as a biomarker in mCRPC. We identified 31 lncRNAs involved in cellular proliferation, tumor metabolism, and invasion-metastasis cascade. SNHG18 and HELLPAR were the highlights of our results. SNHG18 was downregulated in mCRPC and enriched to metastasis signatures. It accurately distinguished both mCRPC and primary CRPC from normal tissue and was associated with epithelial-mesenchymal transition (EMT) and cell-matrix adhesion pathways. HELLPAR consistently distinguished mCRPC from primary CRPC and normal tissue using only its expression. Our results contribute to understanding the regulatory behavior of lncRNAs in mCRPC and indicate SNHG18 and HELLPAR as master regulators and potential new diagnostic targets in this tumor.

Exploring the factors effecting on carbon emissions in each province in China: A comprehensive study based on symbolic regression, LMDI and Tapio models.

Carbon emission (CE) has led to increasingly severe climate problems. The key to reducing CE is to identify the dominant influencing factors and explore their influence degree. The CE data of 30 provinces from 1997 to 2020 in China were calculated by IPCC method. Based on this, the importance order of six factors included GDP, Industrial Structure (IS), Total Population (TP), Population Structure (PS), Energy Intensity (EI) and Energy Structure (ES) affecting the CE of China's provinces were obtained by using symbolic regression, then the LMDI and the Tapio models were established to deeply explore the influence degree of different factors on CE. The results showed that the 30 provinces were divided into five categories according to the primary factor, GDP was the most important factor, followed by ES and EI, then IS, and the least TP and PS. The growth of per capita GDP promoted the increase of CE, while reduced EI inhibited the increase of CE. The increase of ES promoted CE in some provinces but inhibited in others. The increase of TP weakly promoted the increase of CE. These results can provide some references for governments to formulate relevant CE reduction policies under dual carbon goal.

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.