Non-Polynomial Wave Computation through Recurrent Resonant Scattering
Abstract
Structural nonlinearity enables nonlinear input--output mappings to emerge from otherwise linear wave dynamics. Repeated interactions with an input-encoded structure can enhance such mappings, but finite-depth implementations restrict the accessible functional order. Here we show that recurrent scattering in a resonant cavity provides a distinct regime for structural nonlinearity. Repeated interactions are coherently accumulated into a non-polynomial response to structural perturbations. The resulting mapping naturally takes a Kolmogorov--Arnold form: perturbation-induced resonance shifts realize the inner univariate mappings, while the resonant spectral response provides the outer mapping. We identify two complementary physical controls of representation capacity: the resonance linewidth governs the functional richness within each branch, whereas combining multiple branches expands the accessible function space. Microwave-cavity measurements validate the two-stage mapping and demonstrate a two-branch nonlinear computation through XOR classification. Our results connect recurrent resonant scattering with controllable non-polynomial computation in linear wave systems.
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BibTeX
@misc{zhu2026nonpolynomial,
title = {{Non-Polynomial Wave Computation through Recurrent Resonant Scattering}},
author = {Junyu Zhu and Enzong Wu and Xiaomeng Li and Hongsheng Chen and Zuojia Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22745},
eprint = {2609.22745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22745},
}
RIS
TY - UNPB
TI - Non-Polynomial Wave Computation through Recurrent Resonant Scattering
AU - Junyu Zhu
AU - Enzong Wu
AU - Xiaomeng Li
AU - Hongsheng Chen
AU - Zuojia Wang
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22745
UR - https://arxiv.org/abs/2609.22745
AB - Structural nonlinearity enables nonlinear input--output mappings to emerge from otherwise linear wave dynamics. Repeated interactions with an input-encoded structure can enhance such mappings, but finite-depth implementations restrict the accessible functional order. Here we show that recurrent scattering in a resonant cavity provides a distinct regime for structural nonlinearity. Repeated interactions are coherently accumulated into a non-polynomial response to structural perturbations. The resulting mapping naturally takes a Kolmogorov--Arnold form: perturbation-induced resonance shifts realize the inner univariate mappings, while the resonant spectral response provides the outer mapping. We identify two complementary physical controls of representation capacity: the resonance linewidth governs the functional richness within each branch, whereas combining multiple branches expands the accessible function space. Microwave-cavity measurements validate the two-stage mapping and demonstrate a two-branch nonlinear computation through XOR classification. Our results connect recurrent resonant scattering with controllable non-polynomial computation in linear wave systems.
ER -