## 1 Introduction  
Concrete-filled steel tubular (CFST) refers to the composite member formed by filling steel tubular with concrete. CFST makes use of the interaction between concrete and steel tubular under stress to give full play to the advantages of both materials, that is, it not only greatly improves the plasticity and toughness of concrete, but also can avoid or delay the local buckling of steel tubular. CFST has the characteristics of high bearing capacity, good plasticity and toughness, convenient construction, and excellent seismic and refractory performance [1]. Therefore, CFST structures are widely used at home and abroad, of which an important type is the CFST column. CFST columns are mainly divided into square and circular CFST columns based on different sectional forms. Square CFST columns are easy to process and have better stability. Since they are mostly subjected to axial compression, it is necessary to study the ultimate axial capacity of square CFST columns [2]. At present, many experimental studies have been carried out on the mechanical properties of CFST columns under axial compression. [PERSON] et al. [3] presented the behavior of circular CFSTs with various concrete strengths under axial load, and examined the effects of several factors. [PERSON] et al. [4] adopted 16 hollow cold-formed steel tubulars and 48 CFSTs for axial compression tests, and investigated the effects of width/thickness ratio, concrete strength, and geometrical shape of specimens on ultimate loads. The efficient and accurate numerical simulation techniques developed rapidly [5], which were combined with axial compression tests, and fruitful results have been achieved. [PERSON] et al. [6] and [PERSON] et al. [7] respectively established a finite element model considering material nonlinearity and interaction between concrete and steel tubular, and verified the model with experimental data. [PERSON] et al. [8] analyzed the ultimate bearing capacity, failure mode, and load-displacement curve of square thin-walled CFST short columns with reinforcement stiffener at different temperatures using comparative experiments and ABAQUS simulation. Briefly, the ultimate axial capacity is an essential mechanical index to evaluate the performance of CFST columns under axial compression in both laboratory experiments and numerical simulations [9; 10]. However, axial compression tests are time-consuming and laborious. It is also difficult to consider all of the complicated conditions and material properties in numerical simulations. For these purposes, scholars have always been exploring alternative soft computing methods to conveniently acquire the accurate ultimate axial capacity. Mass experimental data have been produced by previous studies, that provide a data basis for mathematical modeling to estimate the ultimate axial capacity of CFST columns. [PERSON] et al. [11] studied the calculation method for ultimate axial capacity of square CFST short columns considering size effect. The calculation formulas in the present codes of different countries were revised by collecting many experimental results. [PERSON] et al. [12] developed a simplified statistical method based on 663 tests to predict the ultimate strength of circular CFST columns under concentric load. The confinement effect on the concrete and the influence of relative slenderness were taken into account. Other simplified calculation methods have also been proposed. For example, a simple method using an equivalent slenderness ratio was suggested by [PERSON] et al. [13] to calculate the load-bearing capacity of CFST laced columns. None of the above-proposed methods have been extensively used due to the limitations of application scope. It is imperative to develop a general and precise method for calculating the ultimate axial capacity. In recent years, with the rapid development of artificial intelligence techniques, machine learning algorithms (MLAs) have been popularized in all walks of life [14].