CD at last epoch of proposed model500.00.10.20.30.40.50.60.70.80.9.001Technical Awards：2022 JSAE Award The Outstanding Technical Paper Award - Surrogate Model Development for Prediction of Car Aerodynamics Using Machine LearningFig.6 Distance function, fl ow fi elds and aerodynamic drag （CD） Table 3 Errors of loss functions in velocity vectors, pressure and 3.2 Flow field validation resultsin datasetFig.7 Histogram of mean absolute error in x-component of Fig.8 Histogram of mean absolute error in pressure on test velocity vector on test casescasesIn addition, because the distance function and CFD results are dimensional information, normalization was performed before using them for learning and testing in this study.A NVIDIA DGX-1™ (1 GPU) was used as a computational resource for learning, and Tensorfl ow 2.0 was employed as a library for machine learning. The time required for learning the fl ow fi eld was approximately 4 days, whereas the time for learning CD was approximately 0.5 days. In addition, by calculating the number of epochs shown in Table 2, it was confi rmed that the values of the fi nal loss function of the three components of the velocity vector, pressure, and CD value are reduced to the extent shown in Table 3.Next, the fl ow fi eld estimated by this method was considered as follows. Each test case had a fl ow velocity vector of 120,000 points (100 × 40 × 30). The mean error of those 120,000 points was considered using the mean absolute error (MAE) shown in equation (1):where ai and yi represent the CFD results and the estimation results of the proposed model, respectively. In addition, n represents the number of grid points, which was 120,000 in this case.The mean absolute error (MAE) of the x-direction component of the velocity vector is presented in Fig. 7. The mean error of the x-component is 0.2–1.1 m/s, which is within the error range of the car speed wind (0.6%–3.3%). In addition, the mean errors of the y- and z-components were smaller than that of the x-component.201510The MAE results for the pressure estimated by the proposed model and evaluated at 120,000 points in the same manner as the velocity vector are presented as a histogram in Fig. 8. The MAE of the pressure is 2.0–9.0 Pa, which is within the error range of approximately 0.3%–1.3% of the dynamic pressure based on the car speed wind. There were no signifi cant differences in the error tendencies among the car types in terms of both velocity and pressure.The pressure and velocity magnitude distributions obtained from the CFD calculations and proposed model are compared in Figs. 9 and 10, respectively. Cases A–D are typical examples of the test cases, and the velocity and pressure errors in each case are shown in Fig. 7 and Fig. 8, respectively. In both Fig. 9 and Fig. 10, the upper rows show the CFD calculation results, whereas the lower rows indicate the estimation results of the proposed model to be compared for each case.8396No.88 (2022) NISSAN TECHNICAL REVIEW
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