Runge-Kutta Random Feature Method for Solving Multiphase Flow Problems of Cells

Cell collective migration plays a crucial role in a variety of physiological processes. In this work, we propose the Runge-Kutta random feature method to solve the nonlinear and strongly coupled multiphase flow problems of cells, in which the random feature method in space and the explicit Runge-Kutta method in time are utilized. Experiments indicate that this algorithm can effectively deal with time-dependent partial differential equations with strong nonlinearity, and achieve high accuracy both in space and time. Moreover, in order to improve computational efficiency and save computational resources, we choose to implement parallelization and non-automatic differentiation strategies in our simulations. We also provide error estimates for the Runge-Kutta random feature method, and a series of numerical experiments are shown to validate our method.