5 citations · 20 across the 19 of their papers we have counts for
20 papers
Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs
Koichi Taniguchi, Sho Sonoda
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, i…
Asymptotically self-similar global solutions for Hardy-Hénon parabolic equations
Noboru Chikami, Masahiro Ikeda, Koichi Taniguchi +1
We construct asymptotically self-similar global solutions to the Hardy-Hénon parabolic equation , , for a large cl…
Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations
Takashi Furuya, Koichi Taniguchi, Satoshi Okuda
Neural operators serve as universal approximators for general continuous operators. In this paper, we derive the approximation rate of solution operators for the nonlinear paraboli…
Reservoir computing with the Kuramoto model
Hayato Chiba, Koichi Taniguchi, Takuma Sumi
Reservoir computing aims to achieve high-performance and low-cost machine learning with a dynamical system as a reservoir. However, in general, there are almost no theoretical guid…
Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
Masahiro Ikeda, Megumi Sano, Koichi Taniguchi
We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \te…
Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain
Masahiro Ikeda, Motohiro Sobajima, Koichi Taniguchi +1
Lifespan estimates for semilinear damped wave equations of the form in a two dimensional exterior domain endowed with the Dirichlet boundary co…