# SP2RINT: Spatially-Decoupled Physics-Inspired Progressive Inverse Optimization for Scalable, PDE-Constrained Meta-Optical Neural Network Training

arXiv: https://arxiv.org/abs/2505.18377 · HTML: https://mlsanity.com/paper/2505.18377/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 21 of 21)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Design of Task-Specific Optical Systems Using Broadband Diffractive Neural Networks](https://mlsanity.com/paper/1909.06553/) (2019)
- [Diffractive all-optical computing for quantitative phase imaging](https://mlsanity.com/paper/2201.08964/) (2022)
- [Computational Imaging Without a Computer: Seeing Through Random Diffusers at the Speed of Light](https://mlsanity.com/paper/2107.06586/) (2021)
- [An Optical Frontend for a Convolutional Neural Network](https://mlsanity.com/paper/1901.03661/) (2018)
- [Metasurface-Enabled On-Chip Multiplexed Diffractive Neural Networks in the Visible](https://mlsanity.com/paper/2107.07873/) (2021)
- [Snapshot Multispectral Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2212.05217/) (2022)
- [Spatially Varying Nanophotonic Neural Networks](https://mlsanity.com/paper/2308.03407/) (2023)
- [Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network](https://mlsanity.com/paper/2203.13482/) (2022)
- [Knowledge Distillation Circumvents Nonlinearity for Optical Convolutional Neural Networks](https://mlsanity.com/paper/2102.13323/) (2021)
- [Classification and reconstruction of spatially overlapping phase images using diffractive optical networks](https://mlsanity.com/paper/2108.07977/) (2021)
- [Physics-aware Differentiable Discrete Codesign for Diffractive Optical Neural Networks](https://mlsanity.com/paper/2209.14252/) (2022)
- [Analysis of Diffractive Neural Networks for Seeing Through Random Diffusers](https://mlsanity.com/paper/2205.00428/) (2022)
- [Rubik's Optical Neural Networks: Multi-task Learning with Physics-aware Rotation Architecture](https://mlsanity.com/paper/2304.12985/) (2023)
- [Pyramid diffractive optical networks for unidirectional image magnification and demagnification](https://mlsanity.com/paper/2308.15019/) (2023)
- [LightRidge: An End-to-end Agile Design Framework for Diffractive Optical Neural Networks](https://mlsanity.com/paper/2306.11268/) (2023)
- [Physics-aware Roughness Optimization for Diffractive Optical Neural Networks](https://mlsanity.com/paper/2304.01500/) (2023)
- [Multi-Dimensional Reconfigurable, Physically Composable Hybrid Diffractive Optical Neural Network](https://mlsanity.com/paper/2411.05748/) (2024)

## Built on by (most cited first, 1 of 1)

- [Democratizing Electronic-Photonic AI Systems: An Open-Source AI-Infused Cross-Layer Co-Design and Design Automation Toolflow](https://mlsanity.com/paper/2601.00130/) (2025)

## Abstract (arXiv)

DONNs leverage light propagation for efficient analog AI and signal processing. Advances in nanophotonic fabrication and metasurface-based wavefront engineering have opened new pathways to realize high-capacity DONNs across various spectral regimes. Training such DONN systems to determine the metasurface structures remains challenging. Heuristic methods are fast but oversimplify metasurfaces modulation, often resulting in physically unrealizable designs and significant performance degradation. Simulation-in-the-loop optimizes implementable metasurfaces via adjoint methods, but is computationally prohibitive and unscalable. To address these limitations, we propose SP2RINT, a spatially decoupled, progressive training framework that formulates DONN training as a PDE-constrained learning problem. Metasurface responses are first relaxed into freely trainable transfer matrices with a banded structure. We then progressively enforce physical constraints by alternating between transfer matrix training and adjoint-based inverse design, avoiding per-iteration PDE solves while ensuring final physical realizability. To further reduce runtime, we introduce a physics-inspired, spatially decoupled inverse design strategy based on the natural locality of field interactions. This approach partitions the metasurface into independently solvable patches, enabling scalable and parallel inverse design with system-level calibration. Evaluated across diverse DONN training tasks, SP2RINT achieves digital-comparable accuracy while being 1825 times faster than simulation-in-the-loop approaches. By bridging the gap between abstract DONN models and implementable photonic hardware, SP2RINT enables scalable, high-performance training of physically realizable meta-optical neural systems. Our code is available at https://github.com/ScopeX-ASU/SP2RINT