Signal identification without signal formulation

When there are signals and noises, physicists try to identify signals by modeling them, whereas statisticians oppositely try to model noise to identify signals. In this study, we applied the statisticians' concept of signal detection of physics data with small-size samples and high dimensions without modeling the signals. Most of the data in nature, whether noises or signals, are assumed to be generated by dynamical systems; thus, there is essentially no distinction between these generating processes. We propose that the correlation length of a dynamical system and the number of samples are crucial for the practical definition of noise variables among the signal variables generated by such a system. Since variables with short-term correlations reach normal distributions faster as the number of samples decreases, they are regarded to be ``noise-like'' variables, whereas variables with opposite properties are ``signal-like'' variables. Normality tests are not effective for data of small-size samples with high dimensions. Therefore, we modeled noises on the basis of the property of a noise variable, that is, the uniformity of the histogram of the probability that a variable is a noise. We devised a method of detecting signal variables from the structural change of the histogram according to the decrease in the number of samples. We applied our method to the data generated by globally coupled map, which can produce time series data with different correlation lengths, and also applied to gene expression data, which are typical static data of small-size samples with high dimensions, and we successfully detected signal variables from them. Moreover, we verified the assumption that the gene expression data also potentially have a dynamical system as their generation model, and found that the assumption is compatible with the results of signal extraction.Comment: 22 pages, 16 figure

Quantitative prediction of fracture toughness (KIc) of polymer by fractography using deep neural networks

Fracture surfaces provide various types of information about fracture. The fracture toughness $${K_{{\rm{I}}c}}$$, which represents the resistance to fracture, can be estimated using the three-dimensional (3D) information of a fracture surface, i.e. its roughness. However, this is time-consuming and expensive to obtain the 3D information of a fracture surface; thus, it is desirable to estimate $${K_{{\rm{I}}c}}$$ from a two-dimensional (2D) image, which can be easily obtained. In recent years, methods of estimating a 3D structure from its 2D image using deep learning have been rapidly developed. In this study, we propose a framework for fractography that directly estimates $${K_{{\rm{I}}c}}$$ from a 2D fracture surface image using deep neural networks (DNNs). Typically, image recognition using a DNN requires a tremendous amount of image data, which is difficult to acquire for fractography owing to the high experimental cost. To compensate for the limited number of data, in this study, we used the transfer learning (TL) method and constructed high-performance prediction models even with a small dataset by transferring machine learning models trained using other large datasets. We found that the regression model obtained using our proposed framework can predict $${K_{{\rm{I}}c}}$$ in the range of approximately 1–5 [MPa\sqrtm] with a standard deviation of the estimation error of approximately $$\pm$$0.37 [MPa\sqrtm]. The present results demonstrate that the DNN trained with TL opens a new route for quantitative fractography by which parameters of fracture process can be estimated from a fracture surface even with a small dataset