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.
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.
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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 Machine Learning
Jun 15
Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems
arXiv:2606. 14079v1 Announce Type: new Abstract: We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces.
arXiv Machine Learning
Jun 30
Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation
arXiv:2512. 09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs).
arXiv AI
Aug 25
FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization
FreKoo++ is a continuous spectral-dynamical framework designed for Temporal Domain Generalization (TDG). It unifies continuous Koopman modal dynamics with adaptive spectral disentanglement, mapping source-domain parameters into a latent space and modeling their evolution as a superposition of learnable continuous modes. The method handles irregular timestamps, supports arbitrary horizon extrapolation, and introduces an adaptive soft spectral weighting mechanism that isolates persistent dynamics from transient noise, achieving state‑of‑the‑art performance on discrete and continuous TDG benchmarks.
arXiv Machine Learning
Jul 7
In-span learning: adapting reduced-order models using their own predictions
arXiv:2607. 02937v1 Announce Type: new Abstract: Reduced-order models compress high-dimensional dynamics into low-dimensional representations that can be evaluated rapidly, but they lose accuracy when online dynamics drift beyond the training data.
arXiv AI
Jul 2
FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
arXiv Machine Learning
Sep 1
Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains
arXiv:2608.29892v1 Announce Type: new Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...
arXiv Machine Learning
Jul 21
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.
arXiv Machine Learning
Sep 25
Functional dynamic mode decomposition: Learning infinite-dimensional systems from data
The paper introduces Functional Dynamic Mode Decomposition (fDMD), extending traditional DMD to infinite-dimensional systems by learning finite-rank operators from functional data such as observables, densities, or wavefunctions. It demonstrates that conventional DMD algorithms are special cases of fDMD and illustrates the approach with examples involving Koopman, Perron‑Frobenius, and Koopman‑von Neumann operators for graphons, ODEs, and SDEs.
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 AI
Jul 14
SFO: Learning PDE Operators via Spectral Filtering
arXiv:2601. 17090v2 Announce Type: replace-cross Abstract: Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps.