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

TL;DR

This paper introduces a novel Runge-Kutta random feature method for efficiently solving complex, nonlinear multiphase flow problems in cellular migration, demonstrating high accuracy and computational efficiency through parallelization and error analysis.

Contribution

The paper presents a new numerical approach combining random features and Runge-Kutta methods for multiphase cell flow problems, with parallelization and error estimation for improved performance.

Findings

Effective handling of nonlinear, strongly coupled PDEs in cell migration.

High accuracy achieved in space and time for multiphase flow simulations.

Parallelization enhances computational efficiency and resource savings.

Abstract

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.