arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
By Zhangyong Liang, Huanhuan Gao
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
By John Chiang
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
By Jian-Feng Cai, Xiliang Lu, Juntao You
arXiv:2609.13569v1 Announce Type: cross
Abstract: Objectives in scientific machine learning are often prescribed as a sum of several terms, such as the residual, boundary, initial, and data losses of...
By Jiahao Zhang, Shiheng Zhang, Guang Lin
arXiv:2610.02182v1 Announce Type: cross
Abstract: Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limit...
By Joohwan Ko, Tetiana Parshakova, Diana Cai, Robert M. Gower
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
By Yuehao Song (School of Automation, Central South University, Changsha, China), Zhong Chen (School of Automation, Central South University, Changsha, China), Lihui Cen (School of Automation, Central South University, Changsha, China), Liang Wu (Johns Hopkins University, Baltimore, USA), Kai Zhang (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, China)