arXiv:2606. 14284v1 Announce Type: cross Abstract: Time series prototype learning is fundamentally challenged by observational ambiguity.
arXiv:2606. 10596v1 Announce Type: cross Abstract: This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$.
This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization.
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.
arXiv:2510. 09685v2 Announce Type: replace-cross Abstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines.
In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world.
arXiv:2607. 27924v1 Announce Type: new Abstract: In the physical world we inhabit, space and time are fundamentally continuous.
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv:2606. 20443v1 Announce Type: cross Abstract: Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data.
arXiv:2602. 02547v2 Announce Type: replace-cross Abstract: Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data.
arXiv:2604. 16232v2 Announce Type: replace-cross Abstract: Understanding natural and engineered systems often relies on symbolic formulations, such as differential equations, which provide interpretability and transferability beyond black-box models.
arXiv:2607. 05280v1 Announce Type: new Abstract: Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences.
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.