用物理约束神经算子加速极紫外光刻掩模仿真，提升效率与精度。
Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation
- 构建基于频域方程的物理信息神经算子，分离横向与轴向维度建模。
- 在16000个掩模设计上训练，预测误差仅约7×10⁻³，媲美精确解。
- 可作为初始值加速精细网格下的背景分解求解器，适合大规模仿真场景。
我们提出一种基于伪谱频域（PSFD）方程的物理信息神经算子（PINO），用于极紫外（EUV）光刻中的电磁散射问题。傅里叶神经算子被分解为二维横向（xy）分支与一维轴向（z）分支，并与背景分解自洽训练，从而保留掩模与多层膜响应间的全矢量耦合，无需采用有限阶次的玻恩近似。该方法显著缩小计算域，降低计算成本。PINO在来自LithoBench库的约16,000个随机采样的掩模设计上训练，未使用预计算的电磁场解。其代理模型对保留掩模图案的散射强度预测，相对于参考PSFD解的平均绝对误差约为7×10⁻³。结合谱阻尼技术，PINO提供的暖启动初始化能加速更细网格下的背景分解PSFD求解器。
原文摘要 · Abstract (English)
We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$) branch and is trained self-consistently with background decomposition.Thus, the full-vector coupling between the mask and the multilayer response is retained without invoking a finite-order Born approximation. In this way, the computational domain size is significantly reduced, thereby lowering the computational cost. The PINO is trained on approximately 16,000 mask designs from the LithoBench library sampled randomly at each training iteration without using precomputed EM field solutions. The PINO surrogate model yields predictions with a mean absolute error of about $7 \times 10^{-3}$ for the scattered intensity of held-out mask patterns relative to the reference PSFD solution. Combined with spectral damping, the PINO warm-start initialization accelerates the background-decomposed PSFD solver on finer discretizations.
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