6 papers
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…
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…
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…