A soft Lasso model for the motion of a ball falling in the non-Newtonian fluid

Abstract

From the mesoscopic point of view, a new concept of soft matching is proposed innovatively. Then a soft Lasso’s approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a discrete iterative algorithm combining the Newton–Stokes term and the soft Lasso’s term is developed to simulate the motion of a ball falling in non-Newtonian fluids. The theory is validated by numerical examples and shows satisfactory results, which exhibit the chaotic phenomena, occasional sudden accelerations and continual random oscillations. These behaviors will maintain for a long time. Furthermore, the pattern of the motion is independent of the initial values as the solution to the Newton–Stokes equation. We find the soft relation in physics to characterize the chaotic phenomena based on the learning method, and improve the method of adding a simple random walk or normal distribution.