arXiv Machine Learning June 4, 2026 By Kelan Gray, Finlay Brown, Nicolas Boull\'e, Matthew J. Colbrook

Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning

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arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

diffusion

arXiv Machine Learning

Jun 30

Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation

arXiv:2606. 29083v1 Announce Type: cross Abstract: Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust.

By George Coote, Matthew J. Colbrook

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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.

By Matthew J. Colbrook, Igor Mezi\'c, Alexei Stepanenko

benchmarks safety data-engineering

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.

By Charles Bokor, Mark Cary, Denise Morrey, Fabrizio Bonatesta

rag safety

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).

By Muhammad Abid, Omer San

rag diffusion benchmarks safety

arXiv Machine Learning

Jul 7

In-span learning: adapting reduced-order models using their own predictions

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By Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy

llms

arXiv Machine Learning

Jul 22

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

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

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Related stories

Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation

Adversarial dynamical systems characterize when data-driven learning succeeds or fails

fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture

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Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics