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

TL;DR

The paper addresses the challenge of training diffractive optical neural networks (DONNs) with physically realizable metasurfaces under Maxwell's equations, which is computationally prohibitive at scale. It introduces SP2RINT, a spatially decoupled, physics-informed progressive inverse optimization that alternates relaxed DONN training with adjoint-based inverse design and employs patch-based transfer-matrix probing to enforce PDE constraints without per-iteration full-wave simulations. SP2RINT delivers up to 1825x speed-ups and achieves digital-comparable accuracy across multiple benchmarks, outperforming heuristic methods by substantial margins (e.g., average improvements of 63.88%). The approach also includes progressive projection, system-level fine-tuning, and transfer learning demonstrations, showing strong potential for scalable, deployable meta-optical neural systems and generalization to other meta-optic devices; code is publicly available.

Abstract

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

Figures (16)

• Figure 1: DONN with multi-layer metasurfaces can be modeled as cascaded transformation $\mathcal{T}$ and diffraction $U$. Metasurface transfer matrix modeling comparison among 3 methods. Our SP2RINT uses banded transfer matrix probing for fast and accurate modeling.
• Figure 2: Proposed spatially-decoupled transfer matrix probing method cuts the metasurface into small patches for patch simulation that reduces complexity from cubic to linear.
• Figure 3: Our proposed SP2RINT framework enables both exploitation and physical feasibility.
• Figure 4: Error sources from ➊ inverse design projection error and ➋ transfer matrix approximation error causing the accuracy degradation from an ideally trained target matrix to a real response of the implemented metasurface.
• Figure 5: Different patch size trades off transfer matrix probing error and runtime.