Oscillatory dynamics arise ubiquitously in nonlinear systems, yet identifying a physically interpretable phase and phase dynamics in nonlinear, high-dimensional oscillations remains a central unresolved problem. Here we establish the principle of a universal dynamical clock, a physical perspective in which oscillations of arbitrary dimensionality and geometry are equivalently represented as uniform rotation through an equant-induced nonlinear viewing coordinate, inspired by Ptolemy's equant and formalised through an areal-uniformity principle reminiscent of Kepler's second law.
arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.
By Zequn He, Celia Reina
arXiv:2410. 11894v3 Announce Type: replace-cross Abstract: Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum.
By Kuang Huang, Dong Heon Cho, Boyuan Chen
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
By Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)
arXiv:2606. 07563v1 Announce Type: cross Abstract: Across machine learning, biology, and physics, independently evolving systems often converge toward strikingly similar high-level structures despite radically different microscopic details.
By Truong Xuan Khanh
arXiv:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.
By Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
By Caleb Munigety
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.
By K. Michael Martini, Eslam Abdelaleem, Paarth Gulati, Ilya Nemenman
arXiv:2608. 02662v1 Announce Type: cross Abstract: Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making.
By Farbod Faraji, Francesco Belardinelli
arXiv:2607. 05127v1 Announce Type: cross Abstract: Understanding the physics of many-body complex dynamical systems is typically non-trivial.
By Domiziano Doria, Matteo Becchi, Giovanni M. Pavan
arXiv:2607. 28977v1 Announce Type: cross Abstract: Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture.
By Jaesung Choi
arXiv:2607. 10285v1 Announce Type: new Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process.
By Max Weinmann, Miriam Klopotek