A novel coupling of noise reduction algorithms for particle flow simulations

Abstract

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

Modeling of Chromium, Copper, Zinc, Arsenic and Lead Using Portable X-ray Fluorescence Spectrometer Based on Discrete Wavelet Transform

“…The process of the Mallat decomposition and reconstruction algorithm is shown in Figure 2 . It is assumed that a conjugate mirror filter is produced by the orthogonal scaling function and wavelet function [ 29 , 30 ]. The scaling coefficients and wavelet coefficients of the WT as c j,k and d j,k , and the recursive formulas are shown in Equations (4) and (5), which enable the calculation { c j,k , d j,k } [ 31 ].…”

Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

“…In order to prevent the noise captured in the POD vectors from spreading into the reconstructed data, the POD vectors should be denoised. Here we employ the wavelet hard-thresholding method for denoising as explained in [27] combined with cycle spinning [4]. Denoising is performed for each POD vector u k individually as detailed in Algorithm 2.…”

“…•ǔ k : the denoised POD vector for i ← 1 to desired number of cycles do v ← cyclically shift u k by i Do wavelet decomposition of v to get the wavelet coefficients w ← the non-zero fine-scale wavelet coefficients σ n ← MAD(w)/0.6745 // MAD represents Median Absolute Deviation T ← σ n 2 log (length of w) // the threshold Set to zero all wavelet coefficients which their absolute value is less than Ť v ← the inverse wavelet transform using the modified wavelet coefficientš u ki ← cyclically shift v by −i enď u k ← the average of allǔ ki returnǔ k Algorithm 2: Wavelet hard-thresholding and cycle spinning for POD vector denoising [27,4] Algorithm 3 summarizes the proposed implementation of Kalman filter and smoother. 6.…”

“…based on which, the error e k between the measured snapshot k and its fbDMD-based prediction is defined as (27) Since the three random variables on the right hand side of equation (27) are white, normally-distributed, and independent from each other, the error e k will also be a white normally-distributed random variable with the covariance S given as…”

Uncertainty Quantification at the Molecular–Continuum Model Interface

“…Mentioned works stressed that the main source of uncertainty in molecular dynamics was due to the atomistic force fields, with the intrinsic noise making only a minor contribution. However, filtering particle-based data can lead to more efficient information extraction and intra-scale communication; a review of various signal processing methods for molecular simulations can be found in Zimoń et al [26,27].…”