  The reconfigurability of radio environments with programmable metasurfaces is
considered a key feature of next-generation wireless networks. Identifying
suitable metasurface configurations for desired wireless functionalities
requires a precise setting-specific understanding of the intricate impact of
the metasurface configuration on the wireless channels. Yet, to date, the
relevant short and long-range correlations between the meta-atoms due to
proximity and reverberation are largely ignored rather than precisely captured.
Here, we experimentally demonstrate that a compact model derived from first
physical principles can precisely predict how wireless channels in complex
scattering environments depend on the programmable-metasurface configuration.
The model is calibrated using a very small random subset of all possible
metasurface configurations and without knowing the setup's geometry. Our
approach achieves two orders of magnitude higher precision than a deep
learning-based digital-twin benchmark while involving hundred times fewer
parameters. Strikingly, when only phaseless calibration data is available, our
model can nonetheless retrieve the precise phase relations of the scattering
matrix as well as their dependencies on the metasurface configuration. Thereby,
we achieve coherent wave control (focusing or enhancing absorption) and
phase-shift-keying backscatter communications without ever having measured
phase information. Finally, our model is also capable of retrieving the
essential properties of scattering coefficients for which no calibration data
was ever provided. These unique generalization capabilities of our pure-physics
model significantly alleviate the measurement complexity. Our approach is also
directly relevant to dynamic metasurface antennas, microwave-based signal
processors as well as emerging in situ reconfigurable nanophotonic, optical and
room-acoustical systems.
