4 papers
Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
Takashi Furuya, Yury Korolev, Takaharu Yaguchi
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-includ…
Approximation Theory of Laplacian-Based Neural Operators for Reaction-Diffusion System
Takashi Furuya, Ryo Ozawa, Jenn-Nan Wang
Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While univ…
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…
Convergences for Minimax Optimization Problems over Infinite-Dimensional Spaces Towards Stability in Adversarial Training
Takashi Furuya, Satoshi Okuda, Kazuma Suetake +1
Training neural networks that require adversarial optimization, such as generative adversarial networks (GANs) and unsupervised domain adaptations (UDAs), suffers from instability.…