## 1 Introduction  
Aerodynamic noise that is generated from aircrafts and automobiles may lead to environmental problems. Therefore, it is important to understand the characteristics of the noise source and reduce the level of noise around those vehicles. The position of the sound source is one of the most important characteristics and it, therefore, has been investigated by aeroacoustic wind tunnel tests using a microphone array consisting of multiple microphones [1, 2, 3, 4]. In general aeroacoustic wind-tunnel testing, a model is installed in an open-jet wind tunnel or a Kevlar-walled wind tunnel, and a microphone array is installed outside of the wind tunnel airflow. Subsequently, the beamforming technique [5, 6, 7, 8, 9, 10, 11] is applied to the acoustic data for the localization of the sound source. In beamforming experiments, a two-dimensional grid corresponding to the sound source localization area is defined in the wind tunnel. Subsequently, the propagation time and the attenuation rate of the acoustic waves from each grid point to a microphone are calculated, and they are used as the steering vector for the sound source localization [5], based on cross-correlation. Here, the acoustic waves that are generated from the sound source in the wind tunnel are refracted by the shear layer, so that the propagation time and the attenuation rate will change, depending on even small change in the wind tunnel test condition or microphone positions. [PERSON] [12] has analytically derived a formula that accounts the effect of the refraction, but there is a problem with this method. The Amiet method [5, 12] requires an iterative calculation for estimating the correction value, and it takes a long time to conduct the exhaustive calculation of steering vectors for the area of the sound source localization. In the onsite quick check of the experimental data, the acceleration of the calculation of the Amiet model is required according to the small change in the wind tunnel test condition or microphone positions. Therefore, the data-driven sparse sampling, which is one of the data-driven approximation, of the Amiet model is proposed in the present study for this purpose. Data-driven sparse sampling [13; 14] is a method that can reconstruct the entire field of large-scale data while using only a small number of sampling points placed at appropriate positions. This method is grounded on the sparseness that the high-dimensional large-scale data can be expressed with only a few numbers of variables, based on the discrete-empirical-interpolation method (DEIM) and QR-DEIM [15; 16]. [PERSON] et al. [17] applied this method to the NOAA-SST and reconstructed the entire distribution of the sea-surface temperature with high accuracy while using just 10 sparse sensors. Those ideas have recently been applied to unsteady fluid dynamic simulations [18] and experiments [19; 20]. In the case of beamforming, the parameters of the positions, the freestream velocity, and the temperature change the relationship between the microphones and sound sources, but the changes in the relationship seem to have some patterns. This suggests that the relationship between the sound sources and microphone array can be expressed by the low-dimensional model, and it may be possible to estimate all of the steering vectors between microphones and sound source locations by just calculating them at appropriate sparse sampling points. This method requires training data calculation, but it can be conducted before the experiments. Therefore, it accelerates the calculation of steering vectors at the onsite quick check of the experimental data, once the training data are prepared. The calculation at appropriate sparse sampling points significantly saves the computational costs and time onsite.