arXiv Machine Learning By Xiaole Zhang, Ziyi Zhang, Zehao Zhao, Stephen Tu, Guannan Qu, Yorie Nakahira, Paul Bogdan

Learning Fractional-Order Dynamics from a Single Trajectory

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arXiv:2609. 18127v1 Announce Type: new Abstract: Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone.

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arXiv Machine Learning
Aug 14

Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection

arXiv:2608. 12879v1 Announce Type: new Abstract: Fractional partial differential equations describe nonlocal dynamics, but discovering them from noisy data is difficult because fractional differentiation amplifies high-frequency measurement noise and the derivative orders are unknown.

By Pongpisit Thanasutives, Yoshinobu Kawahara
arXiv Machine Learning
Aug 27

Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

The paper studies least squares parameter estimation for discrete‑time, unstable, closed‑loop nonlinear stochastic systems with linearly parametrised uncertainty and additive i.i.d. process noise. By perturbing the control policy with exploratory input and assuming a sub‑exponential input‑to‑state growth property, the authors derive non‑asymptotic bounds on the estimation error whenever the state trajectory remains in an informative region of the state space. When the entire state space is informative, the bounds hold with high probability for all time steps, and the authors illustrate the applicability of their results with examples that extend beyond existing work.

By Seth Siriya, Jingge Zhu, Dragan Ne\v{s}i\'c, Ye Pu