Instanton filtering for the stochastic Burgers equation

TL;DR

This paper develops a filtering technique to identify instantons in stochastic Burgers equation simulations, validating the instanton theory by comparing direct numerical results with the Chernykh-Stepanov method.

Contribution

It introduces a novel filtering approach to extract instantons from simulation data, confirming theoretical predictions with numerical evidence.

Findings

Successful extraction of instanton trajectories from simulation data

Strong agreement between filtering results and Chernykh-Stepanov instanton solutions

Demonstration of phases predicted by instanton theory in numerical simulations

Abstract

We address the question whether one can identify instantons in direct numerical simulations of the stochastically driven Burgers equation. For this purpose, we first solve the instanton equations using the Chernykh-Stepanov method [Phys. Rev. E 64, 026306 (2001)]. These results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations. Using this approach we can extract the entire time history of the instanton evolution which allows us to identify the different phases predicted by the direct method of Chernykh and Stepanov with remarkable agreement.