[00980] Recent Advances in Applied Mathematics including adopting machine learning and deep learning
Session Time & Room : 1D (Aug.21, 15:30-17:10) @E504
Type : Proposal of Minisymposium
Abstract : Applied mathematics is the field of mathematical methods and statistical reasoning to solve practical problems of a scientific or decision-making nature in a variety of subjects, engineering, medicine, physical and biological sciences. In particular, Industrial mathematics is one of the fastest-growing branches in applied mathematics and plays a growing role in developing robotics and automation systems, mechanical engineering, medicine, and others. It is concerned with developing and finding the most efficient mathematical methods to solve problems arising in recent.
This session consists of recent research trends on applied mathematics, numerical analysis to find optimal solutions, and statistical methodology for uncertainty inference including machine learning (deep learning) applications.
[01658] A hybrid difference method and its postprocessings for second order elliptic problems
Format : Talk at Waseda University
Author(s) :
Dongwook Shin (Ajou University)
Youngmok Jeon (Ajou University)
Eun-Jae Park (Yonsei University)
Abstract : In this talk, we investigate a new method, the hybrid difference method, proposed by S., Jeon, and Park (Appl. Math. Comput., 2022), for second order elliptic problems. The hybrid difference method is a finite difference method that is based on the hybrid discontinuous Galerkin method introduced by Jeon and Park (SINUM, 2010). The HD method allows arbitrarily high-order approximations, and the local conservation property holds. The HD method allows arbitrarily high-order approximations, and satisfies the local conservation property. Additionally, it can significantly reduce the global degrees of freedom by the static condensation via Schur complement similar to the HDG method. In the recent work, we have extended and improved the HD method by introducing additional conditions. This new generalized method can be seen as the method introduced by Jeon, Park, and S. (Comput. Methods Appl. Math., 2017) with the addition of a simple postprocessing. To increase computational efficiency, we also introduce a residual type error estimator that allows for the use of adaptive algorithms. The proposed method can be extended to more complex domain geometries through simple modifications, although the local conservation property may not hold in these cases and thus requires further postprocessing. Several numerical experiments are presented to show the performance of the proposed method, which support our theoretical findings.
[05287] Predicting Thermoelectric Material Properties using Machine Learning
Format : Talk at Waseda University
Author(s) :
YunKyong Hyon (National Institute for Mathematical Sciences)
Abstract : According to the development of machine learning technologies, the application of machine learning is already very active in all research areas. Material design requires a lot of calculation and computer resources in its classical process, but the process and period of material development can be shortened by using machine learning methodologies. We present a machine learning model that predicts the properties of materials required for the development of thermoelectric materials and its performance.
[05338] Classification of respiratory sounds using deep learning methods
Format : Talk at Waseda University
Author(s) :
Sunju Lee (National Institute for Mathematical Sciences (NIMS))
Abstract : Auscultation with a stethoscope has been an essential part of diagnosing patients with respiratory diseases and providing first aid. However, accurate interpretation and diagnosis of auscultation sounds relies on the expertise of clinicians, so it is important to develop an artificial intelligence-based diagnosis support system using respiratory sounds. In this talk, we propose a deep-learning based classification model for respiratory sounds recorded in the clinical setting.
[05339] Interpretable Classification for Multivariate Gait Analysis
Format : Talk at Waseda University
Author(s) :
Soon-Sun Kwon (Department of Mathematics/Artificial Intelligence, Ajou University, South Korea)
Abstract : Motivated by gait data from both the normal and the cerebral palsy (CP) patients group with various gross motor function classification system (GMFCS) levels, we propose a multivariate functional classification method to investigate the relationship between kinematic gait measures and GMFCS levels. A sparse linear functional discrimination framework is utilized to achieve an interpretable prediction model. The method is generalized to handle multivariate functional data and multi-class classification. The method yields superior prediction accuracy and provides easily interpretable discriminant functions. And it will help clinicians to diagnose CP and assign an appropriate GMFCS level in a more consistent and mathematical evidence.
