14:30 〜 14:45
▼ [14p-A205-4] Visualization of free energy landscape in spinodal decomposition using persistent homology combined with unsupervised machine learning
キーワード：Materials informatics, topological data analysis
Persistent homology is a powerful tool to extract topological features from the microstructure, such as the size, shapes, and connectivity of holes. It can also be combined with machine learning to find hiding correlations between variables in the data set. In this work, we prepared spinodal decomposition images using phase-field calculation and applied persistent homology to study the relationship between free energy and morphology. The image sets were prepared using different values for the gradient energy coefficient ( $κ$), a parameter that controls the probability of phase separation. We prepared 5 sets of 400 images for each value of $κ$ and we computed the total free energy at each step to confirm the convergence of the calculation. After concluding the simulation, persistent homology was applied to image sets to obtain persistent diagrams (PD). The PD maps the topological features of an image in a set of points ("birth","death") that can be later analyzed using machine learning or other informatics technique. In our case, an unsupervised machine learning algorithm called kernel principal component analysis (PCA) was implemented to search for non-linear correlations between the PDs. One surprising result is that the contribution of these two variables is near 1.0, which implies that a large amount of image data could successfully be embedded in a low-dimensional manifold.Concretely, the separation of $κ$ and continuity of energy value were successfully visualized. Thus, we believe that this approach can be used in experimental images, and it might be helpful to improve the analysis and to extract information of hidden parameters.