arXiv AI July 23, 2026 By Kanad Sen, Romit Maulik

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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arXiv Machine Learning

Aug 31

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...

By Rajat Sarkar, Venkataramana Runkana, Souvik Chakraborty

llms benchmarks

arXiv Machine Learning

3d ago

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.

By Lucas Gerken Starepravo, Henry Broadley, Steven Lind, Jack R. C. King

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.

By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)

diffusion

arXiv AI

Sep 15

LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction

arXiv:2609.14977v1 Announce Type: cross Abstract: Finite element stress fields often exhibit strong local non-smoothness, where stress concentrations near holes, notches, and loading regions induce s...

By Chen Zeng, Qiao Wang

arXiv Machine Learning

Sep 16

A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction

arXiv:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....

By Zeyang Huang, Angelos Chatzimparmpas, Thomas H\"ollt, Takanori Fujiwara

rag

arXiv Machine Learning

Sep 10

ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows

arXiv:2609.08947v1 Announce Type: cross Abstract: Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, th...

By Th\'eodore Michel, Antoine Campos, Alban Dujardin, Henry Areiza, Philippe Meliga, Elie Hachem

llms benchmarks

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Related stories

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

Learning Spectrally Optimised Mesh-Free Discretisations

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction

A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction

ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows