Proper orthogonal decomposition (POD) and its extension based on time-windows have been shown to greatly improve the effectiveness of recovering smooth ensemble solutions from noisy particle data. However, to successfully de-noise any molecular system, a large number of measurements still need to be provided. In order to achieve a better efficiency in processing time-dependent fields, we have combined POD with a well-established signal processing technique, wavelet-based thresholding. In this novel hybrid procedure, the wavelet filtering is applied within the POD domain and referred to as WAVinPOD. The algorithm exhibits promising results when applied to both synthetically generated signals and particle data. In this work, the simulations compare the performance of our new approach with standard POD or wavelet analysis in extracting smooth profiles from noisy velocity and density fields. Numerical examples include molecular dynamics and dissipative particle dynamics simulations of unsteady force- and shear-driven liquid flows, as well as phase separation phenomenon. Simulation results confirm that WAVinPOD preserves the dimensionality reduction obtained using POD, while improving its filtering properties through the sparse representation of data in wavelet basis. This paper shows that WAVinPOD outperforms the other estimators for both synthetically generated signals and particle-based measurements, achieving a higher signal-to-noise ratio from a smaller number of samples. The new filtering methodology offers significant computational savings, particularly for multi-scale applications seeking to couple continuum informations with atomistic models. It is the first time that a rigorous analysis has compared de-noising techniques for particle-based fluid simulations.
Zimoń, M. J., Reese, J. M., & Emerson, D. R. (2016). A novel coupling of noise reduction algorithms for particle flow simulations. Journal of Computational Physics, 321, 169–190. https://doi.org/10.1016/j.jcp.2016.05.049