Dynamic Kuramoto-Hodge Operators for PDEs on Complex Geometries and Topologies
cs.LG, cs.AI
Submitted: 2026-09-27
Updated: 2026-09-27
Code: https://github.com/xiangMXPXAI/Dynamic-Kuramoto-Hodge-Operators
Terminology
Sources
- The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics
- Topological Neural Operators
- Winfree Oscillatory Neural Network
- Discrete Exterior Calculus
- Simplicial Neural Networks
- Topological Deep Learning: Going Beyond Graph Data
- Neural Operator: Graph Kernel Network for Partial Differential Equations
- Fourier Neural Operator for Parametric Partial Differential Equations
- Geometry-Informed Neural Operator for Large-Scale 3D PDEs
- Domain Agnostic Fourier Neural Operators
- Artificial Kuramoto Oscillatory Neurons
- Learning Mesh-Based Simulation with Graph Networks
- Kuramoto Orientation Diffusion Models
- Topology-Preserving Neural Operator Learning via Hodge Decomposition
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