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.

翻译：细胞集体迁移在多种生理过程中起着关键作用。本文提出龙格-库塔随机特征方法以求解非线性强耦合的细胞多相流问题，该方法在空间上采用随机特征方法，在时间上采用显式龙格-库塔方法。实验表明，该算法能有效处理具有强非线性的时间依赖偏微分方程，并在空间和时间上均达到较高精度。此外，为提高计算效率并节约计算资源，我们在模拟中选择了并行化与非自动微分策略。本文同时给出了龙格-库塔随机特征方法的误差估计，并通过一系列数值实验验证了所提方法的有效性。