Unified, Verifiable Neural Simulators for Electromagnetic Wave Inverse
  Problems
Charles Dove Jatearoon Boondicharern Laura Waller
Simulators based on neural networks offer a path to orders-of-magnitude
faster electromagnetic wave simulations. Existing models, however, only address
narrowly tailored classes of problems and only scale to systems of a few dozen
degrees of freedom (DoFs). Here, we demonstrate a single, unified model capable
of addressing scattering simulations with thousands of DoFs, of any wavelength,
any illumination wavefront, and freeform materials, within broad configurable
bounds. Based on an attentional multi-conditioning strategy, our method also
allows non-recurrent supervision on and prediction of intermediate physical
states, which provides improved generalization with no additional
data-generation cost. Using this O(1)-time intermediate prediction capability,
we propose and prove a rigorous, efficiently computable upper bound on
prediction error, allowing accuracy guarantees at inference time for all
predictions. After training solely on randomized systems, we demonstrate the
unified model across a suite of challenging multi-disciplinary inverse
problems, finding strong efficacy and speed improvements up to 96% for problems
in optical tomography, beam shaping through volumetric random media, and
freeform photonic inverse design, with no problem-specific training. Our
findings demonstrate a path to universal, verifiably accurate neural surrogates
for existing scattering simulators, and our conditioning and training methods
are directly applicable to any PDE admitting a time-domain iterative solver.