# Physics-constrained neural networks for surrogate modeling of lossless periodic structures

arXiv: https://arxiv.org/abs/2606.28119 · HTML: https://mlsanity.com/paper/2606.28119/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 36 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 1 of 1)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)

## Abstract (arXiv)

We introduce a physics-constrained neural network for the rapid prediction of rigorous coupled-wave analysis outputs in the form of Jones matrices. Starting from energy conservation in lossless layered periodic structures, we use the fact that the scattering outputs lie on a Stiefel manifold. This energy constraint is enforced as a hard condition by projecting onto the manifold using differentiable symmetric orthogonalization. The resulting surrogate enforces energy conservation by construction while preserving differentiability for gradient-based inverse design. The performance and generality of the proposed approach are demonstrated through the inverse design of a diffractive waveguide combiner for augmented reality glasses.