arXiv Machine Learning
Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs
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arXiv Machine Learning
Sep 30
Learning Spectrally Optimised Mesh-Free Discretisations
The paper introduces Spectrally Optimised Neural Discretisations (SpeND), a mesh‑free framework that learns discretisation weights from local stencil geometry on unstructured point clouds. By embedding discrete moment conditions into the network architecture, SpeND guarantees polynomial consistency and allows the weights to be optimised for spectral accuracy over a chosen wavenumber band, using an unsupervised Fourier‑mode loss. The resulting operators are PDE‑agnostic, perform well on Poisson, Burgers, and Navier–Stokes equations, and can reduce wall‑clock time by 3–20× compared to existing mesh‑free methods at the same accuracy.
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 AI
Jul 24
Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery
arXiv:2607. 20857v1 Announce Type: cross Abstract: Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data.
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
Jun 2
Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator
arXiv:2604. 01802v2 Announce Type: replace Abstract: Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications.
arXiv AI
Jul 15
Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.