5:15 PM - 7:15 PM
[PEM11-P01] Accelerating Nonlinear Heat Conduction Simulations in High-Temperature Regions Using Deep Learning
Keywords:Deep learning, surrogate model, numerical simulation, nonlinear heat conduction, solar flare
Fast and highly accurate simulations are required to elucidate the physical mechanisms of solar flares and utilize them for predictive purposes. In solar flare simulations, magnetohydrodynamic (MHD) equations including the effect of nonlinear heat conduction are numerically solved. However, the short timescale of heat conduction necessitates a tiny time step, increasing the number of integration steps. The Super TimeStepping (STS) method, which allows time steps larger than the CFL conditions for solving parabolic partial differential equations, is often employed to reduce computational costs. However, numerical errors increase as the time step becomes larger. Recently, surrogate models that replace numerical integration steps with deep-learning-based approximations have also attracted attention as an alternative; however, they have been applied to only a few MHD simulations of solar flares.
In this study, we aimed to accelerate the calculations for the nonlinear heat conduction in solar flare simulations by developing a deep learning model that learns simulation data and predicts temperature profiles after a certain elapsed time. We designed a 19-layer convolutional neural network (CNN) based on an autoencoder. This model takes temperature distribution and conduction coefficients as inputs. The outputs are the temperature distribution 1000 time steps ahead of the input temperature distribution in the direct simulations. One-dimensional nonlinear heat conduction simulation data were used for training. Gaussian functions were applied for the initial profiles, and the conduction coefficient was randomly set within the range of 0.1 to 5.0.
The proposed model achieved high accuracy, with a Mean Absolute Percentage Error (MAPE) of 1.28% compared with the results of direct simulations as the ground truth. Moreover, the deep learning model's error relative to direct simulations was smaller than that of the STS method. Our results showed that the surrogate model can achieve higher accuracy and computational efficiency compared with the STS method for nonlinear heat conduction simulations. This approach holds potential for improving the efficiency and accuracy of simulations in the high-temperature regions of solar flares.
In this study, we aimed to accelerate the calculations for the nonlinear heat conduction in solar flare simulations by developing a deep learning model that learns simulation data and predicts temperature profiles after a certain elapsed time. We designed a 19-layer convolutional neural network (CNN) based on an autoencoder. This model takes temperature distribution and conduction coefficients as inputs. The outputs are the temperature distribution 1000 time steps ahead of the input temperature distribution in the direct simulations. One-dimensional nonlinear heat conduction simulation data were used for training. Gaussian functions were applied for the initial profiles, and the conduction coefficient was randomly set within the range of 0.1 to 5.0.
The proposed model achieved high accuracy, with a Mean Absolute Percentage Error (MAPE) of 1.28% compared with the results of direct simulations as the ground truth. Moreover, the deep learning model's error relative to direct simulations was smaller than that of the STS method. Our results showed that the surrogate model can achieve higher accuracy and computational efficiency compared with the STS method for nonlinear heat conduction simulations. This approach holds potential for improving the efficiency and accuracy of simulations in the high-temperature regions of solar flares.