The paper introduces Dynafit, a kernel-based method for classifying trajectories produced by distinct nonlinear dynamical systems. It learns a distance metric by approximating the Koopman operator, enabling classification in a feature space without explicit dimensionality. The authors demonstrate Dynafit on logistic map chaos detection, handwritten dynamical pattern recognition, and visual dynamic texture classification.
By Dominique Martinez
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
By YongKyung Oh, Dong-Young Lim, Sungil Kim
The paper introduces a new framework for learning continuous-time diffeomorphic image registration by modeling a non-autonomous ODE as a two-parameter flow map. By enforcing cocycle consistency, the method learns flow maps without time discretization or velocity integration during training, enabling efficient inference with few compositions. Experiments on nine datasets show consistent alignment improvements, including a 2.1% Dice gain on brain MRI, 12% TRE reduction on lung CT, and 2.6% Dice improvement on cardiac MRI and ultrasound.
By Mohammadjavad Matinkia, Nilanjan Ray
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
arXiv:2609.38049v1 Announce Type: new
Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
By Fred Xu, Thomas Markovich, Barbora Barancikova, Yizhou Sun
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