Neural Spectral Element Methods
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Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks
arXiv:2606.02335v1 Announce Type: cross Abstract: The Neural Spectral Element Method (NSEM) evaluates each network only at fixed Legendre-Gauss-Lobatto quadrature nodes and replaces all derivative calls with precomputed spectral differentiation matrices. The resulting deterministic loss enables limited-memory BFGS (L-BFGS) to reach residuals of 10^-9 to 10^-10. A Kosloff-Tal-Ezer coordinate map resolves electrochemical boundary layers, while a mesh-free neural mortar framework couples...
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
Announce Type: new Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional input, it employs $d$ independent subnetworks -- each acting on a single coordinate -- and constructs basis functions via element-wise multiplication of their outputs....
Monte Carlo Steklov Operators for Large-Scale Geometry Processing in the Wild
arXiv:2606.05581v1 Announce Type: new Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes. Intrinsic operators, in particular the Laplacian, underlie methods that require invariance to isometry and have hence been employed in many algorithms for shape analysis, learning, and editing. However, intrinsic methods are predicated on assumptions that quickly become brittle when working with in-the-wild geometry, where (i) mesh quality is not guaranteed, and (ii)...
Non-destructive Identification of Oyster Species is possible from Hyperspectral Images with Machine Learning
arXiv:2605.30811v1 Announce Type: new Abstract: Differentiating between oyster species is important for developing new commercial oyster species suited to production systems and is critical for traceability in seafood supply chains. Common methods, such as DNA profiling, are destructive and time consuming. The possibility of using hyperspectral imaging (HSI) for discriminating between Black-Lip rock (BL) and Sydney rock (SR) oysters was investigated.