Most learning architectures for dynamical systems rely on generic nonlinear function approximation, often requiring high model complexity to capture structured behaviors. In this work, we propose an alternative paradigm in which modeling capability arises primarily from structure rather than from expressive nonlinearities.
arXiv:2412. 12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods.
By Arunabh Singh, Joyjit Mukherjee
arXiv:2604. 17121v3 Announce Type: replace Abstract: Transformers encode structure in sequences via an expanding contextual history.
By Michael C. Mozer, Shoaib Ahmed Siddiqui, Rosanne Liu
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
By Xizhe Wang, Xiaobin Song, Hongbo Zhao, Qingshan Jia, Qianchuan Zhao, Hao Sun, Benben Jiang
arXiv:2607. 09801v1 Announce Type: new Abstract: Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements.
By Yi Zhu, Su Chen, Xiaojun Li, Xiuli Du
arXiv:2508. 12448v2 Announce Type: replace-cross Abstract: In-context learning (ICL) lets large language models (LLMs) solve new tasks from prompts alone, across an ever-widening range of domains, yet the mechanisms underlying this ability remain poorly understood.
By Yeongwoo Song, Jaeyong Bae, Dong-Kyum Kim, Hawoong Jeong