Spectral estimation from simulations via sketching

TL;DR

This paper demonstrates that sketching techniques can effectively compress simulation data while maintaining high accuracy in estimating spectral properties like autocorrelation and power spectral density, outperforming previous methods.

Contribution

It introduces the novel application of sketching for spectral estimation from simulation data, providing theoretical guarantees and practical validation.

Findings

Spectral density estimated with 90% accuracy using only 10% of data

Sketching outperforms previous methods in spectral estimation accuracy

Theoretical guarantees support the effectiveness of sketching in this context

Abstract

Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can be used to compress simulation data and still accurately estimate time autocorrelation and power spectral density. For a given compression ratio, the accuracy is much higher than using previously known methods. In addition to providing theoretical guarantees, we apply sketching to a molecular dynamics simulation of methanol and find that the estimate of spectral density is 90% accurate using only 10% of the data.