Machine Learning-Driven Cooling Window Design Beyond Hyperbolic Metamaterials

Analytical multilayers designed under quarter-wave conditions, such as antireflective coatings and distributed Bragg reflectors, generally perform effectively within narrow spectral bands but often face challenges in meeting multispectral demands. In contrast, machine learning (ML)-driven inverse design enables exploration of vast parameter spaces to realize tailored spectral responses across multiple bands. However, whether ML-optimized multilayers can outperform analytical designs under identical material and thickness constraints often remains an open question. Here, we experimentally validate the superiority of ML-driven design through a metal/dielectric multilayer cooling-window coating that simultaneously requires high average visible transmittance (AVT) and high average near-infrared reflectance (ANR). By integrating a factorization machine with simulated annealing, we discovered optimized aperiodic ZnS/Ag multilayers and benchmarked them against periodic hyperbolic metamaterial (HMM) counterparts. Under a 156 nm thickness constraint (equivalent to two ZnS/Ag pairs in a HMM), the ML design achieved 0.57 AVT and 0.98 ANR, surpassing the HMM reference (0.49 AVT, 0.83 ANR). With an extended thickness of 300 nm, the ML-optimized coating further improved to 0.79 AVT by suppressing Fabry-Perot resonances while maintaining high ANR (0.97). Furthermore, the ML-driven multilayers exhibited tunable transmitted colors spanning the full visible gamut, whereas the HMM counterparts were restricted to specific hues. Both ML and HMM designs were fabricated on glass, and measured spectra confirmed the superior optical and thermal performance of the ML approach. These findings establish ML-driven inverse design as a powerful route to ultrathin, manufacturable, and color-tunable cooling-window coatings that can contribute to urban energy savings.