DOI: 10.5281/zenodo.8378015
title: Phase field modelling combined with data-driven approach to unravel the orientation influenced growth of interfacial Cu6Sn5 intermetallics under electric current stressing

description: <strong>Description:</strong> The datasets are constituted by two folders, namely, (A) data_features_and_metric.zip and (B) grain_area_prediction.zip. <strong>(A) data_features_and_metric.zip:</strong> The following are the contents of this folder (i) <em>grainTheta.csv file</em> : The "grainTheta.csv" file consists the datasets generated from multiple phase field simulations. Name of the columns in the csv file are: <strong>gnid </strong>= grain id number "n", <strong>ntheta = </strong>orientation angle of n<sup>th</sup> grain (<sup>o</sup>); <strong>nltheta </strong>= orientation angle of grain to the left of n<sup>th</sup> grain (<sup>o</sup>); <strong>nrtheta </strong>= orientation angle of grain to the right of n<sup>th</sup> grain (<sup>o</sup>); <strong>j </strong>= current density (A/m<sup>2</sup>);<strong> t =</strong> time (s); <strong>area</strong> = area of n<sup>th</sup> grain (m<sup>2</sup>);<strong> tl</strong> = horizontal length of the top edge of grain "n" (m) ; <strong>bl </strong>= horizontal length of the bottom edge of grain "n" (m) The features gnid, ntheta, nltheta and nrtheta for a given observation are determined during the design of initial conditions of the corresponding phase field simulation. The value of "j" for the observation is determined via the boundary condition in the same numerical simulation. The result from the finite element method based phase field simulation has provided the numerical quantities for t, area, tl and bl attributes. The multiple observations in the data file have been obtained from multiple phase field simulations. (ii) <em>imc_theta.ipynb, imc_theta.py and imc_theta.html files</em>: These files contain the code to build the Pearson's Correlation Coefficient (PCC) heatmap analysis of the data contained in grainTheta.csv file. (iii) <em>comparison_mse.csv</em>: This data file includes the information about mean square error for training data (tmse) and mean square error for validation data (vmse) at Epoch = 199 resulting from 10 different artificial neural network (ANN) models distinguished by 10 different values of learning rates (lr) . Thus, the name of the columns in this csv file are <strong>modelno</strong>, <strong>lr</strong>, <strong>tmse</strong> and <strong>vmse</strong>. (iv) <em>mse_comparison.gnu</em>: This file consists the codes required to output a png image from the data provided in comparison_mse.csv<em>. </em> (v) train_loss.csv and val_loss.csv: These files consist of the data of tmse and vmse at all points of Epochs for the ANN model with lr = 2.5E-4 . Thus, the first column in train_loss.csv file corresponds to tmse whereas the second column is Epochs number. Similarly, vmse and Epochs represent the two columns in val_loss.csv file. (vi) <em>mse_lr2p5e-4.gnu</em> : This file consists the codes required to output a png image from the data provided in train_loss.csv and val_loss.csv<em>. </em> <strong>(B) grain_area_prediction.zip:</strong> Inside this folder, there is a folder named "prediction_of_grain_area" consisting of the following files: <em>initial_area.csv file</em>: This file consists the value of the initial grain area of grain 4. It is a constant at all orientation angle. <em>predicted_result_00_5e4.csv</em>: This file consists of the prediction result of grain 4 area (at different orientation angles and t = 1250 s) for grain 3 and grain 5 at orientation angles of 0<sup>o</sup> and 0<sup>o </sup>respectively, and for applied current density of 5.0E+4 J/m<sup>2</sup> . <em>predicted_result_00_5e5.csv</em>: This file consists of the prediction result of grain 4 area (at different orientation angles and t = 1250 s) for grain 3 and grain 5 at orientation angles of 0<sup>o</sup> and 0<sup>o </sup>respectively, and for applied current density of 5.0E+5 J/m<sup>2</sup> . <em>predicted_result_9090_5e4.csv</em>: This file consists of the prediction result of grain 4 area (at different orientation angles and t = 1250 s) for grain 3 and grain 5 at orientation angles of 90<sup>o</sup> and 90<sup>o </sup>respectively, and for applied current density of 5.0E+4 J/m<sup>2</sup> . <em>predicted_result_9090_5e5.csv</em>: This file consists of the prediction result of grain 4 area (at different orientation angles and t = 1250 s) for grain 3 and grain 5 at orientation angles of 90<sup>o</sup> and 90<sup>o </sup>respectively, and for applied current density of 5.0E+5 J/m<sup>2</sup> . <em>area_00_adj.gnu</em> : This gnu file contains the code to produce the png image from the data contained in <em>predicted_result_00_5e4.csv </em>and<em> predicted_result_00_5e5.csv </em>. The information about the initial area of grain 4 is obtained from <em>initial_area.csv</em> file by the code. <em>area_9090_adj.gnu</em> : This gnu file contains the code to produce the png image from the data contained in <em>predicted_result_9090_5e4.csv </em>and<em> predicted_result_9090_5e5.csv </em>. The information about the initial area of grain 4 is obtained from <em>initial_area.csv</em> file by the code.
description: This work is supported by National Natural Science Foundation of China (Grant Number: 51205135 and Grant Number : 52101035) and the National Science Centre, Poland (SONATA BIS grant, UMO-2021/42/E/ST5/00339).