# Unified, Verifiable Neural Simulators for Electromagnetic Wave Inverse Problems

arXiv: https://arxiv.org/abs/2404.00545 · HTML: https://mlsanity.com/paper/2404.00545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 44 references that are in the map.
- First posted on arXiv 31 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [Global optimization of dielectric metasurfaces using a physics-driven neural network](https://mlsanity.com/paper/1906.04157/) (2019)
- [SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering](https://mlsanity.com/paper/1705.04281/) (2017)
- [Imaging through scattering media via spatial-temporal encoded pattern illumination](https://mlsanity.com/paper/2112.13303/) (2021)

## Abstract (arXiv)

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.