用物理约束提升神经网络对周期结构光响应的预测速度与精度
Physics-constrained neural networks for surrogate modeling of lossless periodic structures
- 将能量守恒作为硬约束，通过可微正交化投影到斯特费尔流形
- 预测结果严格满足能量守恒，且保留梯度可导性用于逆向设计
- 成功应用于增强现实眼镜衍射波导合束器的快速逆向优化
我们提出一种物理约束神经网络（PCNN），用于快速预测无损层状周期结构中严格耦合波分析（RCWA）的琼斯矩阵输出。基于无损结构的能量守恒特性，发现RCWA输出位于斯特费尔流形上，通过可微正交化将其投影到该流形，以硬约束形式强制能量守恒。所提出的代理模型在构造上保证能量守恒，同时保持可微性，适用于基于梯度的逆向设计。该方法在增强现实眼镜用衍射波导合束器的逆向设计中验证了其性能与通用性。
原文摘要 · Abstract (English)
We introduce a physics-constrained neural network (PCNN) for the rapid prediction of rigorous coupled-wave analysis (RCWA) outputs in the form of Jones matrices. Starting from energy conservation in lossless layered periodic structures, we use the fact that RCWA 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.
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