Cauchyformer: Few-Shot Spectrum Inference for Photonic Metasurfaces via Mixture of Cauchy.

Inferring hard-to-access spectra from simpler measurements is a fundamental challenge across photonics, materials science, chemistry, and biology. Intrinsic cross-frequency correlations encode rich information about structure, composition, and dynamics; utilizing these relations enables rapid characterization, screening, and design without expensive iterative simulations or experiments. A representative and highly demanding setting is metasurface photonics, where structural optimization relies on large-scale partial differential equation (PDE) solvers, rendering ultrabroadband full-wave electromagnetic simulations prohibitively expensive. Existing time-series and signal forecasting approaches typically require large training data sets, yet spectral data is often scarce and costly to acquire. Moreover, these data-driven models lack explicit awareness of the underlying spectral physics. In this work, we introduce Cauchyformer, a physics-informed framework for accurate few-shot spectra-to-spectra inference. At its core, Cauchyformer employs a Mixture-of-Cauchy (MoC) mechanism that explicitly encodes Cauchy-Lorentz resonances, representing spectra as superpositions of Cauchy basis functions. Combined with patching and bidirectional attention modules to capture local and global dependencies across frequencies and channels, Cauchyformer enables accurate spectrum inference from minimal training data. Experiments on simulated and fabricated metasurfaces demonstrate state-of-the-art performance in fast and reliable prediction of resource-intensive high-frequency spectra from more accessible low-frequency optical responses, even with scarce training samples. Owing to its generic architecture, Cauchyformer can be readily adapted to a wide range of multispectral inference and spectrometry tasks, including material characterization, environmental sensing, and proteomics.