Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations

The paper addresses the Maxey‑Riley‑Gatignol equations, which describe the motion of spherical inertial particles in a fluid and include the Basset force—a history‑dependent integral term. Because this term complicates numerical solutions, it is often omitted, yet it significantly influences particle trajectories. The authors propose using universal differential equations, specifically neural networks, to approximate the Basset force, thereby converting the equations into a system of ordinary differential equations solvable by standard methods such as Runge‑Kutta.

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