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

2025-05-23

AI Summary

Optical neural networks (ONNs) face a fundamental trade-off between physical realizability and computational scalability during training. Method: This work formulates ONN design as a PDE-constrained inverse optimization problem. We propose a spatially decoupled, progressive inverse-design framework: (i) relax physical constraints via trainable banded transmission matrices; (ii) enforce realizability through alternating optimization and physics-based calibration; and (iii) accelerate computation via field-locality-driven block-parallelization, integrated with adjoint-based PDE-constrained optimization. Contribution/Results: Our method achieves digital-neural-network-level accuracy across diverse tasks. Training is 1825× faster than simulation-based closed-loop approaches. To our knowledge, this is the first framework enabling large-scale, end-to-end trainable, and physically realizable metasurface-based photonic neural networks.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

DONNs harness the physics of light propagation for efficient analog computation, with applications in 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 training methods directly optimize a physically implementable metasurface using adjoint methods during end-to-end DONN training, but are inherently 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.

Problem

• Challenges in training DONNs for metasurface structure determination
• Heuristic methods yield unrealizable designs and performance degradation
• Simulation-in-the-loop methods are computationally prohibitive and unscalable

Innovation

• Spatially decoupled progressive training framework
• Banded transfer matrices for relaxed constraints
• Parallel inverse design with local field interactions