Unified, Verifiable Neural Simulators for Electromagnetic Wave Inverse Problems (2404.00545v1)

Abstract: 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.