Particle-based fluid simulations can be utilised to study phenomena ranging from galaxyscale, using smoothed particle hydrodynamics, plasma physics with particle-in-cell methods, aerospace re-entry problems, using direct simulation Monte Carlo, down to chemical, biological and fluid properties at the nanoscale with molecular dynamics and dissipative particle dynamics. The information generated by particle methods, such as molecular dynamics, is converted to macroscopic observables by means of statistical averaging. A significant drawback of nano- or micro-scale modelling is the substantial noise associated with particle techniques, which disturbs the analysis of the results. The uncertainty in the mean of the ensemble is due to fluctuations caused e.g. by additional forcing terms (thermostats). Extracting the genuine information from indirect, noisy measurements is analogous to solving the ill-posed statistical inverse problem, where the object of interest is not easily accessible. The presence of noise in the data can be reduced by averaging over a large number of samples, but the computational intensity of the simulations would then be substantially increased. In order to improve the efficiency of estimating the unknown structure from the disturbed observations, a number of decomposition techniques have been applied, including: proper orthogonal decomposition, singular spectrum analysis, random QR de-noising, wavelet transform, and empirical mode decomposition. In the present work, the strengths and weaknesses of each approach, and their extensions to solving statistical inverse problems for particle simulations, are evaluated. Furthermore, we propose several novel combinations of these methods, that have the capability to improve the signal-to-noise ratio and reduce the computational cost.
|Date of Award||1 Apr 2015|
- University Of Strathclyde
|Sponsors||EPSRC (Engineering and Physical Sciences Research Council)|
|Supervisor||Jason Reese (Supervisor) & Thomas Scanlon (Supervisor)|