# Wall effects of eccentric spheres machine learning for convenient computation

## TL;DR

This paper enhances analytical methods and employs neural networks to efficiently quantify wall effects on eccentric spheres within spherical boundaries, achieving high accuracy and enabling quick predictions for various configurations.

## Contribution

It introduces an improved analytical approach combined with neural network modeling to accurately and efficiently evaluate wall effects on eccentric spheres in confined spherical systems.

## Key findings

- Model achieves ~0.001% error within training domain.
- Model maintains ~0.05% error when extrapolated to infinite plane.
- Enables convenient prediction of wall effects for arbitrary configurations.

## Abstract

In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical. Therefore, quantifying the wall effects from an outer spherical boundary on the motion of an internal eccentric sphere is very useful. However, when the two spheres are not concentric, the problem becomes non-trivial. In this paper we improve existing analytical methods to evaluate these wall effects and then train a feed-forward artificial neural network within a broader model. The final model generally performed with $\sim 0.001\%$ error within the training domain and $\sim 0.05\%$ when the outer spherical wall was extrapolated to an infinite plane. Through this model, the wall effects of an outer spherical boundary on the arbitrary motion of an internal sphere for all experimentally achievable configurations can now be conveniently and efficiently determined.