4 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 la…
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…
Theoretical Error Analysis of Entropy Approximation for Gaussian Mixtures
Takashi Furuya, Hiroyuki Kusumoto, Koichi Taniguchi +2
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, t…