Learning qBIC Resonances across Metasurface Families in Dielectric Fourier Space

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

Reconfigurable intelligent surfaces (RISs) modify signal reflections to enhance wireless communication capabilities. Classical RIS phase optimization is highly non convex and challenging in dynamic environments due to high interference and user mobility. Here we propose a hierarchical multi-objective quantum metalearning algorithm that switches among specific quantum paths based on historical success, energy cost, and current data rate. Candidate RIS control directions are arranged as switch paths between quantum neural network layers to minimize inference, and a scoring mechanism selects the top performing paths per layer. Instead of merely storing past successful settings of the RIS and picking the closest match when a new problem is encountered, the algorithm learns how to select and recombine the best parts of different solutions to solve new scenarios. In our model, high-dimensional RIS scenario features are compressed into a quantum state using the tensor product, then superimposed during quantum path selection, significantly improving quantum computational advantage. Results demonstrate efficient performance with enhanced spectral efficiency, convergence rate, and adaptability.

Machine learning surrogates based on neural operators have shown broad applicability in solving forward PDE problems. However, eigenvalue problems, in which an eigenparameter and one of several valid eigenmodes must be simultaneously solved, remain difficult because standard operator learning formulations assume a unique input-output map. This work demonstrates that Fourier Neural Operators (FNOs), combined with wavelet-based encodings of PDE inputs, can learn and predict multiple eigenmodes of the elastic wave equation, corresponding to deformation modes of acoustic waves propagating through arbitrary metamaterial geometries. We provide a mechanistic explanation and experimental evidence for why wavelet encodings are well matched to the dual spatial-spectral structure of the FNO, enabling deterministic mode selection on both continuous-valued and binary-valued geometries within a single model, and for why prediction accuracy varies with geometric discontinuities. For metamaterial design, the resulting surrogate accelerates the simulation stage of the design cycle by three orders of magnitude relative to finite element analysis on a consumer-grade CPU, while preserving high fidelity. These results also carry broader implications for designing input encodings in other multi-mode PDE solvers based on spectral neural operators.