## 1 Introduction  
With the rapid development of the electromagnetic wave technology, people rely more and more on mobile phones. The electromagnetic radiation generated by the use of mobile phones has increasingly serious adverse effects on important parts of the human body, such as the head and the heart, which has also become a cause for concern [1, 2]. A portion of in vitro and in vivo research studies have indicated that electromagnetic radiation directly affects biological systems [3, 4]. The Institute of Electrical and Electronics Engineers (IEEE) and The International Commission for Non-ionizing Radiation Protection (ICNIRP) have formulated relevant human electromagnetic field exposure limit standards [5, 6], which have been applied in the research on the safety assessment of antenna electromagnetic exposure [7]. Experiments have shown that even the current acceptable radiation value for mobile phones will lead to metabolic changes in the brain, with unknown results. With the acceptable electromagnetic radiation value, difficulties in the design of mobile phones and antennas have become more acute. For SAR measurement methods, international standards specify the relevant measurement criteria [8]. The quantification of the SAR of mobile phone electromagnetic radiation by the human head, has high time and economic costs; so, it is necessary to use computer simulations to simulate the electromagnetic radiation emitted by mobile phones to the human head. A heterogeneous source term identified by medical imaging using pixel information quantified into greyscale numbers and Hounsfield units has been very helpful in quantifying the SAR [9, 10]. Even if laboratories use the same mobile phone model, the same material parameters, and the same electromagnetic simulation software, the calculation results of electromagnetic radiation simulation calculations will contain errors due to the uncertainty of the electromagnetic parameters [11]. Obviously, the uncertainty quantification of the electromagnetic radiation from mobile phones to the human head has become an urgent problem to be solved, but this is a challenging task. In this paper, the gPC method was used to construct a SAR computational proxy model for UQ. The core idea of the gPC method is to represent the random response as a linear combination of polynomials [12; 13]. The Monte Carlo (MC) method is based on the law of large numbers and requires an extremely accurate analysis, which implies a large computational cost [14]. Compared with the MC method, the gPC method has a relatively high calculation accuracy and does not need to calculate the derivative information of the function. In addition, once the function expansion of the random response is completed, any statistics can be easily obtained. However, the computation amount of the gPC method will increase significantly with the increase of the polynomial expansion order. In order to improve the computational efficiency, [PERSON] et al. proposed a variety of adaptive regression methods [15; 16], which retain the main terms and low-order cross terms in the orthogonal polynomial expansion, while ignoring some unimportant high-order cross terms. Thus, the calculation efficiency is greatly improved. The MC method is a traditional UQ method used to calculate the statistical characteristics of a model. In electromagnetic simulations, the calculation cost of the model is very high; so, it is necessary to properly select the sample size of the MC method. In other engineering applications, usually 10,000 runs of the simulation in the MC method were verified [17; 18]. In this paper on electromagnetic radiation, considering the computational cost and accuracy, 1000 runs of the MC method were used in the simulation model to verify the effectiveness of the above gPC method. The Sobol method is the most classic global sensitivity analysis method [19].