Kuramoto Model

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Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies
Sep 27, 2026Xiang Li, Yue SongKuramoto Model Hodge Decomposition
Tsinghua University · Beijing University of Chemical Technology
The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics
Aug 10, 2026Petr Badolia, Leonid Obukhov, Dmitry Bylinkin +1Dynamical Systems Kuramoto Model
Basic Research of Artificial Intelligence Laboratory (BRAIn Lab) · Innopolis University
Temporal-Causal Unity as an Operational Framework for Collective Dynamics: Causal-Progress Clocks, Synchronization, and Polarization
Jul 21, 2026Jian Liu, Dong SunDynamical Systems Kuramoto Model
Xintong Zhima (Beijing) Technology Co., Ltd., Beijing, China
On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers
Jul 20, 2026Sixu Li, Thomas Jacob Maranzatto, Jan Peszek +5Dynamical Systems Kuramoto Model
University of Wisconsin–Madison, Department of Statistics · University of Maryland, Department of Electrical and Computer Engineering · University of Warsaw, Institute of Applied Mathematics and Mechanics +2
Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs
Jul 15, 2026Manuel Fernandez, Yizhe ZhuKuramoto Model Graph Clustering
Department of Mathematics, University of Southern California
Attention by Synchronization in Coupled Oscillator Networks
Jun 10, 2026Fabio Pasqualetti, Taosha GuoSoftmax Attention Dynamical Systems
Electrical Engineering and Computer Science University of California, Irvine
Kuramoto Attention: Synchronizing Self-Attention on the Torus
Jun 10, 2026Joshua NunleyDynamical Systems Kuramoto Model
Department of Informatics, Luddy School of Informatics, Computing, and Engineering Cognitive Science Program Indiana University Bloomington
Information-Geometric Optimization on Spheres
May 27, 2026Vladimir Ja\' cimovićInformation Geometry Kuramoto Model
Faculty of Natural Sciences and Mathematics University of Montenegro Cetinjski put bb., 81000 Podgorica Montenegro
The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networks
Apr 11, 2026Mani Rash AhmadiEquilibrium Propagation Oscillatory Neural Networks
Calibur Labs
Oscillator-Based Associative Memory with Exponential Capacity: Theory, Algorithms, and Hardware Implementation
Apr 1, 2026Arie Ogranovich, Taosha Guo, Arvind R. Venkatakrishnan +3Kuramoto Model Associative Memory
Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, 93106, USA · Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA, 92697, USA
Identifiability and amortized inference limitations in Kuramoto models
Mar 23, 2026Emma Hannula, Jana de Wiljes, Matthew T. Moores +2Kuramoto Model Amortized Inference
LUT University, Yliopistonkatu 34, Lappeenranta, 53850, Finland · TU Ilmenau, Ehrenbergstraße 29, Ilmenau, 98693, Germany · University of Cambridge, Herschel Road, Cambridge, CB3 9AL, United Kingdom
Synchronization-based clustering on the unit hypersphere
Mar 5, 2026Zinaid Kapić, Aladin Crnkić, Goran MaušaKuramoto Model Clustering
Faculty of Technical Engineering, University of Bihać, Bihać
Selective Synchronization Attention
Feb 16, 2026Hasi HaysKuramoto Model Self-Attention
Department of Chemical Engineering, University of Arkansas, Fayetteville, AR 72701, USA

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Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies

Xiang Li, Yue Song

Tsinghua University · Beijing University of Chemical Technology

Kuramoto Model Hodge Decomposition PDE Operator Learning Neural Operators

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Learning PDE operators on complex domains requires capturing interactions among fields on vertices, edges, and faces, alongside global responses shaped by topology. Existing neural operators accommodate irregular geometries but often overlook these distinct field supports or their condition-dependent coupling. We introduce the Dynamic Kuramoto--Hodge Operator (DKHO), which combines topology-constrained interactions with learned coordination. DKHO encodes conditions on their native cochain supports, evolves Kuramoto-inspired relation states through the boundary and coboundary operators that compose the Dirac operator, and decodes non-harmonic and harmonic responses in orthogonal Hodge subspaces. Topology thus determines where information can flow, while learned dynamics adapts how it is exchanged to each PDE instance. Across porous-medium Darcy flow, torus transport--diffusion, and cavity magnetostatics, DKHO-large reduces prediction error by approximately 61% on average over leading baselines, while DKHO-small remains competitive using only 11.5--24.3% as many parameters. These results suggest that coupling topological structure with adaptive dynamics provides an effective inductive bias for accurate and parameter-efficient PDE operator learning on complex geometries and topologies.