Spectral estimation from simulations via sketching

Highlights: • Time autocorrelation functions and power spectral density are common outcomes of large numerical simulations. • When there are many particles or grid points, only very short lag autocorrelations are possible due to the required storage. • Randomized sketching techniques can be used to reduce the cost of storage. • These new techniques have theoretical guarantees and better practical performance than existing techniques. 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.