Rapid portabilization of elasto-chemical evolution data for dental Ti-Cr alloy microstructure through sparsification and tensor computation

c_theta_interpolation_function_data.csv: Interpolation function is utilized in phase field model to interpolate the material properties along the interface region. In this work, the corresponding material property that has been  interpolated is the elasticity tensor. The csv file (c_theta_interpolation_function_data.csv) consists of the data of the interpolation function h(theta,c)  given by the expression h = 1/(1+ exp(-theta(2c-1))).  The input feature "c" in the weighted input feature for the sigmoidal function is the mole fraction of Chromium in the two metastable phase regions in the binary Ti-Cr alloy undergoing phase decomposition. The "c" column in the table represents the data of Chromium composition. For the present study,  the value of weighted parameter in the input feature is taken as equal to  10 i.e.  theta = 10 . Hence, the column h(10,c) represents the data of the interpolation function used by the phase field simulation (Eq. 8 in the paper).  To illustrate on how the choice of theta alters the values of h,  this csv file also presents four additional columns of h corresponding to different constant values of theta (theta = 5, 15, 20 and 50). The steepness of the sigmoidal interpolation function increases as theta increases, and the graphical representation of the table can be accessed at  https://interpolationfunction.streamlit.app/. 

spatial-coordinates_composition_data_Figure4c.csv: This file contains the data of  Fig. 4(c) which is the result of the microstructure reconstruction after Tucker decomposition with 10 % sparsification for t = 1 h 23 min 20s. The spatial distribution of Cr composition is sufficient to represent the microstructural information for the binary Ti-Cr alloy. That is the data  of spatial coordinates and mole fraction of Cu at each coordinate is sufficient to represent this microstructure. Thus, the csv file consists of the following three columns : X-Coordinate (nm), Y-Coordinate (nm) and Cr_MoleFraction.  The unit for the values of X and Y coordinates is nm. The mole fraction is unitless. 

bulk_free_energy.csv: The file contains the data of the coefficients alpha, beta, gamma, delta, epsilon and ceq in the equation for  bulk thermodynamic free energy ( F_{chem}) at T = 700.15 K. Mathematically,   F_{chem} = f_{chem}* Vmol  where Vmol is the molar volume of a phase.  The expression for molar bulk chemical free energy is: F_{chem} = alpha*(epsilon*c - ceq)^2 + beta*(epsilon*c - ceq) + beta*(epsilon*c - ceq)^6 + delta.  

statistical_metrics_comparison.zip:This folder consists of three files that compares the outcome of tensor impainting results of Canonical Polyadic (CP) and Tucker methods for three  sparsity values ( 10 %, 15 % and 25%). Each of the files corresponds to the sparsity value, and so the names of of the files are statistical_metrics_10percent.csv, statistical_metrics_15percent.csv and statistical_metrics_20percent.csv. Four types of statistical techniques are considered: root mean square error (RMSE), microstructural similarity (micro sim), blob detection via deviation quantified from Determinant of Hessian (DoH), and Shape Index. The first three methods: RMSE, microstructural similarity and blob detection via DoH are used quantitatively to compare the tensor inpainted images with the benchmark image from phase field method. Shape index is used to perform qualitative analysis, and it has been inferred that both CP and Tucker methods based decomposition and subsequent reconstruction/inpainting are in the acceptable from the viewpoint of tracking the curvature of interfaces. For 10% sparsity, the Tucker method is found to produce better results even if both CP and Tucker produce acceptable ones.