This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory data points along with their time derivatives are used.
arXiv:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
By Yao Cheng Li, Ana Larra\~naga, Steven L. Brunton, Urban Fasel
The paper proposes a new receding‑horizon algorithm for the Linear Quadratic Regulator (LQR) with unknown dynamics, inspired by REINFORCE. It removes the need for two‑point gradient estimates and does not require a stable initial policy, while maintaining the same order of sample complexity. A refined analysis of error propagation via the Riccati operator’s contraction under Riemannian distance yields improved sample complexity and convergence guarantees.
By Amirreza Neshaei Moghaddam, Alex Olshevsky, Bahman Gharesifard
The paper proposes a new interpretable machine learning approach for discovering unknown nonlinear ordinary differential equations from a single state trajectory. It differs from existing methods by deriving its formulation from Functional Analysis and Operator Theory and by defining a cost function as an integral distance between functions rather than a discrete error sum. An incremental learning algorithm enables online updates, allowing simultaneous identification of both system dynamics and external time‑varying forces, with numerical examples illustrating its benefits.
By Seyyed Shaho Alaviani, Yongzhi Qu, Gregory W. Vogl
arXiv:2606. 15690v1 Announce Type: new Abstract: Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity.
By Filippo Zacchei, Ana Larra\~naga, Attilio Frangi, Andrea Manzoni, Steven L. Brunton
arXiv:2606. 23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics.
By Mat\'ias G\'omez-Aedo, Behzad Azmi, Yuyang Huang, Dante Kalise, Karl Kunisch