3 papers
math.NA2025
Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
Oussama Ounissi, Masato Kimura, Hirofumi Notsu
In this study, we consider a spring-block system that approximates a -dimensional linear elastic body, where or . We derive a matrix as the spring constan…
math.AP2025
On the well-posedness of a Hele-Shaw-like system resulting from an inverse geometry problem formulated through a shape optimization setting
Julius Fergy Tiongson Rabago, Masato Kimura
The purpose of this study is twofold. First, we revisit a shape optimization reformulation of a prototypical shape inverse problem and briefly propose a simple yet efficient numeri…
cs.LG2024
Universal approximation property of ODENet and ResNet with a single activation function
Masato Kimura, Kazunori Matsui, Yosuke Mizuno
We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is consider…