arXiv Machine Learning
Jun 4
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture
arXiv:2607. 17990v1 Announce Type: new Abstract: Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency.
Related stories
arXiv Machine Learning
Jun 24
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
arXiv:2407. 06312v2 Announce Type: replace-cross Abstract: Many systems resist analytical modeling, making data-driven inference of dynamics important.
arXiv AI
Aug 18
Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.
arXiv AI
Aug 18
PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models
arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv AI
Aug 5
A neural operator framework for data-driven discovery of stability and receptivity in physical systems
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv Machine Learning
Sep 10
Minimum distance classification for nonlinear dynamical systems
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.
arXiv Machine Learning
Sep 10
Geometric Dictionary Learning of Dynamical Systems with Optimal Transport
The paper introduces DOODL, a framework that learns a dictionary of spectral dynamics to represent related dynamical systems as points on a low‑dimensional manifold in operator space. By constraining operator estimation to this learned manifold, DOODL provides compact, interpretable embeddings and enables fast, accurate operator estimation from short, partially observed trajectories. Experiments on metastable Langevin dynamics and turbulent plasma simulations show that DOODL achieves one to two orders of magnitude lower errors than independent estimation methods, especially in low‑data regimes.
arXiv Machine Learning
Aug 7
Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
arXiv:2608. 05416v1 Announce Type: new Abstract: Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem?
arXiv AI
Jul 7
When is a System Discoverable from Data? Discovery Requires Chaos
arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
arXiv AI
Jul 23
Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses
arXiv:2607. 19387v1 Announce Type: cross Abstract: Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields.
arXiv Machine Learning
Jul 31
On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems
arXiv:2607. 28080v1 Announce Type: cross Abstract: We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems.
arXiv Statistics ML
Aug 25
Symbolic Neural ODEs: Learning interpretable models from time-series data
arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...