Pychastic: Precise Brownian Dynamics using Taylor-It\=o integrators in Python

TL;DR

Pychastic is a Python package that enables fast, precise Brownian Dynamics simulations with hydrodynamic interactions, leveraging Taylor-Itô integrators and automatic differentiation for improved accuracy and usability.

Contribution

The paper introduces Pychastic, a Python tool that implements Taylor-Itô integrators for Brownian Dynamics, simplifying complex calculations and achieving high performance.

Findings

Achieves simulation speeds comparable to lower-level languages.

Handles divergence of mobility tensor and discontinuous trajectories effectively.

Utilizes automatic differentiation to simplify integrator implementation.

Abstract

In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the It\=o calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-It\=o integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.