On the connection between dissipative particle dynamics and the It\^o-Stratonovich dilemma

TL;DR

This paper links the systematic errors in Dissipative Particle Dynamics simulations to the Itô-Stratonovich dilemma caused by multiplicative noise, and proposes a new algorithm that significantly improves accuracy and efficiency.

Contribution

It introduces a novel DPD simulation algorithm that addresses the Itô-Stratonovich dilemma, reducing errors and increasing efficiency.

Findings

New algorithm improves accuracy by nearly tenfold.

Simulation efficiency nearly doubles with the new method.

Systematic errors are primarily due to multiplicative noise in Langevin equations.

Abstract

Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system particles, thus allowing them to overlap. This supposedly permits relatively large integration time steps, which is an important feature for simulations on large temporal scales. In practice, however, an increase in the integration time step leads to increasingly larger systematic errors in the sampling statistics. Here, we demonstrate that the prime origin of these systematic errors is the multiplicative nature of the thermal noise term in Langevin's equation, i.e., the fact that it depends on the instantaneous coordinates of the particles. This lead to an ambiguity in the interpretation of the stochastic differential Langevin equation, known as the It\^o-Stratonovich dilemma. Based on insights from previous studies of the dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an order of magnitude improvement in accuracy, and nearly twice the efficiency of commonly used DPD Langevin thermostats.