Direct statistical simulation of the Lorenz63 system

TL;DR

This paper applies direct statistical simulation to the Lorenz63 system, solving for its low-order statistics directly rather than through long-term numerical integration, and compares the results to traditional methods.

Contribution

It introduces a novel application of DSS to the Lorenz63 system with different truncation choices and compares the outcomes to standard simulation results.

Findings

DSS can effectively compute low-order statistics of Lorenz63

Different truncation methods influence the accuracy of the statistics

Fixed points of the statistics can be obtained via evolution or iteration

Abstract

We use direct statistical simulation (DSS) to find the low-order statistics of the well-known dynamical system, the Lorenz63 model. Instead of accumulating statistics from numerical simulation of the dynamical systems, we solve the equations of motion for the statistics themselves after closing them by making several different choices for the truncation. Fixed points of the statistics are obtained either by time evolving, or by iterative methods. Statistics so obtained are compared to those found by the traditional approach.