The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti
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)
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
By Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba, Zachary D. Danziger, Deniz Erdogmus
arXiv:2410.23667v2 Announce Type: replace
Abstract: Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known con...
By Alistair White, Anna B\"uttner, Maximilian Gelbrecht, Valentin Duruisseaux, Niki Kilbertus, Frank Hellmann, Niklas Boers
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis
arXiv:2609.38877v1 Announce Type: new
Abstract: Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Exi...
By Wenjie Wang, Yuanyuan Wang, Zixiang Jiang, Shaoan Xie, Mingming Gong