Denoising methods for thermomechanical decomposition for quasi-equilibrium molecular dynamics simulations

In this work, we applied robust denoising methods well established in the signal processing field for the thermomechanical decomposition of velocity data obtained from molecular dynamics (MD) simulations. In the decomposition, the atomic velocity was assumed to be the sum of the mechanical velocity and the thermal velocity, which can be linked to the stress and temperature field at the continuum scale, respectively. For the quasi-equilibrium process, with the thermal velocity treated as the Gaussian distributed stationary noise with zero mean and a positive variance that is linearly proportional to temperature and mechanical velocity as the clean signal, the velocity decomposition can be recasted into a denoising problem, for which powerful denoising methods have been developed to estimate a clean signal from noisy data. We investigated the widely-used linear parametric real-domain, linear nonparametric Fourier-based, and nonlinear nonparametric wavelet-based denoising methods, first on their theoretical properties and then made comparsion among them for denosing some synthetic noisy 1-dimensional (1D) data generated from MD simulations. The nonlinear wavelet-based thresholding estimator possessed better optimality properties than the other estimators, and also outperformed the other estimators in the synthetic data test. A further test comparing the various denoising methods for an adiabatic shear crack nucleation and propagation process simulated using MD simulations showed better performance by the wavelet-based denoisng method. Results from this work reveal good potential of applying wavelet-based denoising method to the study of thermomechanical processes simulated using MD simulations.