Enhanced walk on spheres algorithm with generative adversarial networks for convection-diffusion simulation

This study introduces an enhanced Walk on Spheres (WOS) algorithm, integrated with Generative Adversarial Networks (GANs), to simulate convection-diffusion processes involving velocity fields. The traditional WOS algorithm handles isotropic diffusion well but struggles with convection-diffusion scenarios. By training GANs to generate spherical distribution data, the extended WOS algorithm adapts to varying boundary conditions and convection influences. Our approach segments the computational domain into multiple radial intervals, training a specific GAN model for each interval to capture particle dynamics accurately. This segmentation allows the algorithm to select the most suitable model in real-time, enhancing simulation accuracy and adaptability. Experimental results show significant improvements in computational efficiency and accuracy compared to traditional Monte Carlo methods, with the enhanced WOS algorithm reducing runtime by approximately 40% while maintaining high precision. The algorithm’s robustness and flexibility make it valuable for various applications, including ecological dynamics, disease modeling, and fluid dynamics. Future work will focus on optimizing the algorithm for highly irregular media and expanding its application to broader scientific and engineering problems.