Ultra-Efficient Reconstruction of Anisotropic Hyperuniform Continuous Random Fields in 2D and 3D via Generalized Spectral Filtering

Abstract: Hyperuniform continuous random fields suppress large-scale fluctuations while preserving rich local disorder, making them highly attractive for next-generation photonic, thermal and mechanical materials. However, traditional reconstruction techniques often suffer from limited spectral control or excessive computational cost, especially in high-resolution 2D and 3D settings. In this work, we present an ultra-efficient generative algorithm based on generalized superellipse spectral filtering, which allows independent tuning of isotropic and anisotropic spectral envelopes without resorting to costly iterative schemes. We demonstrate our method on a comprehensive set of 2D and 3D examples, showing precise manipulation of spectral band shape and orders-of-magnitude speedup compared to existing approaches. Furthermore, we explore the effect of simple thresholding on the generated fields, analyzing the morphological features and power-spectrum characteristics of the resulting two-phase maps. Our results confirm that the proposed framework not only accelerates hyperuniform field synthesis but also provides a versatile platform for systematic study of binary microstructures derived from continuous designs. This work opens new avenues for large-scale simulation and optimized design of advanced hyperuniform materials.