arXiv Machine Learning September 18, 2026 By Jiaquan Zhang, Chaoning Zhang, Shuxu Chen, Meng Ye, Xiaofeng Zhang, Qiang He, Weifeng Huang, Guoqing Wang, Yang Yang, Caiyan Qin

Hypernetwork-Parameterized Spatially Adaptive Neural Operators for PDE Learning

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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.

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