用神经网络近似流体中粒子的历史力，让复杂方程变简单可解。
Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
- 用通用微分方程和神经网络逼近历史效应项
- 将积分型方程转化为可常规求解的常微分方程组
- 适合研究颗粒运动且希望避开复杂数值计算的研究者
Maxey-Riley-Gatignol 方程（MaRGE）用于描述流体中球形惯性粒子的运动。该方程包含一个体现尾迹和边界层历史效应的巴塞特力（Basset force），即粒子受力依赖于其历史轨迹，导致数值求解困难。因此，该力常被忽略，尽管已有大量证据表明它对粒子运动模式具有显著的定性和定量影响。本文基于通用微分方程思想，提出一种利用神经网络近似历史项的方法，将 MaRGE 转化为一组可通过标准数值方法（如 Runge-Kutta 法）求解的常微分方程。
原文摘要 · Abstract (English)
The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods.
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