7 papers
Constructive Universal Approximation by Infinite-Dimensional Neural Networks via Gaussian-Weighted Ridgelet Transform
Sho Sonoda, Luca Galimberti, Yuanchao Xu +2
Neural networks whose inputs are functions, as in operator learning, are usually shown to be universal by existence arguments, either by reduction to finite-dimensional networks or…
How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?
Xiaoyuan Cheng, Wenxuan Yuan, Boyang Li +7
Diffusion policy sampling enables reinforcement learning (RL) to represent multimodal action distributions beyond suboptimal unimodal Gaussian policies. However, existing diffusion…
Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections
Yuanchao Xu, Itsushi Sakata, Isao Ishikawa
Finite-dimensional Koopman eigenvalues do not characterize resolvent growth, particularly for nonnormal compressions. We study the singular-value structure of empirical Koopman fin…
Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspective
Yuanchao Xu, Fengyi Li, Masahiro Fujisawa +3
We propose Koopman Spectral Wasserstein Gradient Descent (KSWGD), a particle-based generative modeling framework that learns the Langevin generator via Koopman theory and integrate…
Reinforcement-Learning-Guided Data-Driven Estimation of Spectral Properties of Stochastic Koopman Semigroups
Yuanchao Xu, Jing Liu, Weiping Ding +2
Koopman spectral analysis turns nonlinear stochastic dynamics into a linear evolution of observables and gives access to decay rates, oscillatory modes, and metastable behavior. In…
A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…
ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals
Yuanchao Xu, Kaidi Shao, Nikos Logothetis +1
Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global li…