arXiv Machine Learning
Function-Space Transformer with Adaptive Anchors
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arXiv AI
Aug 17
ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv Machine Learning
Sep 1
Tracing distinguishability through transformer processing with stochastic LayerNorm
arXiv:2608.30720v1 Announce Type: new Abstract: Representational similarity is foundational to analyses of deep networks, yet distances between point-valued representations are not intrinsically tied...
arXiv Machine Learning
Sep 18
Hypernetwork-Parameterized Spatially Adaptive Neural Operators for PDE Learning
The paper introduces Hypernetwork-Parameterized Spatially Adaptive Neural Operators (SANO) for learning partial differential equations (PDEs) with spatial heterogeneity. SANO replaces spatially shared parameterization with a continuous field of location-dependent operator parameters, generated by a coordinate-conditioned hypernetwork and interpolated via a Hyper-Neural Element mechanism. Experiments on 1‑, 2‑, and 3‑dimensional PDEs and perforated-domain elliptic benchmarks demonstrate that SANO consistently outperforms existing neural‑operator, hypernetwork‑based, and physics‑informed baselines.
Hugging Face Trending Papers
Jun 22
Neural Operator Processes for Probabilistic Operator Learning under Partial Observations
Neural operators learn mappings between function spaces, but are typically developed with dense input-output training fields and fully observed inputs at inference. Many scientific problems require instead predicting solution fields from sparse, irregular, or partial observations under uncertainty.
arXiv Machine Learning
Jun 2
Revisiting Neural Processes via Fourier Transform and Volterra Series
arXiv:2606. 01172v1 Announce Type: new Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering.
arXiv Machine Learning
Sep 17
HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometries
HiLNO is a hierarchical latent neural operator that builds a fine‑to‑coarse‑to‑fine latent space and incorporates multi‑scale supervision and anisotropic Gaussian attention to preserve spatial information in PDE solutions with multiscale structures. The hierarchy reduces information loss during compression, while multi‑scale supervision aligns intermediate predictions with downsampled targets, and anisotropic attention facilitates feature transfer across scales. Experiments on standard PDE benchmarks and a large‑scale automotive aerodynamics task show that HiLNO achieves competitive accuracy while cutting parameter count by 84.4% and FLOPs by 69.2% compared with LinearNO, and it generalizes effectively to unseen spatial resolutions.