用动态生成训练样本,让神经网络加速求解复杂光波散射逆问题。
Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems

- 训练时动态寻找难例,提升模型泛化能力。
- 可处理超41,772个变量,推理速度提升1.29至26.5倍。
- 适合需要快速设计大尺寸光学器件的研究者。
神经网络代理模型正取代传统电磁波仿真器(如有限差分时域法,FDTD),通过预训练网络实现波散射正向与逆向问题的快速求解。然而,非递归的单步代理模型此前仅能扩展至数十个模拟变量。本文提出一种新算法,在训练过程中并行生成具有代表性的难例,而非随机采样。该方法利用梯度上升搜索折射率与源配置,定位代理模型与全波真值仿真器差异显著的情况,并结合源与真值归一化及演化重放数据集,稳定并加速学习。基于此,我们训练出一个二维波散射的单步代理模型,支持高达41,772个可控变量,包括密集自由配置的折射率网格与复数源。该代理模型在结构化与非结构化样本上均表现稳健,且具备归纳外推能力,无需重训即可扩展至超300万变量。应用于大规模正向仿真与逆向设计,实现了自由形式分束器与梯度折射率(GRIN)透镜(最大98波长)的设计,性能媲美或优于FDTD方法,速度提升达1.29×至26.5×,为光子逆向设计等波散射逆问题提供了高效、鲁棒、可扩展的神经仿真路径。
原文摘要 · Abstract (English)
Neural network surrogates are an emerging alternative to traditional electromagnetic wave simulators like finite-difference time-domain (FDTD); their goal is to replace rigorous physical simulations with pre-trained neural networks that solve wave-scattering forward and inverse problems orders of magnitude faster. However, nonrecurrent, single-step surrogates have scaled only to a few tens of simulation variables. Here, we show that this barrier can be overcome by dynamically generating salient training examples during training, rather than randomly sampling the large space of possible examples. We introduce an algorithm that runs in parallel with surrogate training, using gradient ascent to search refractive-index and source configurations for cases where the surrogate disagrees with a full-wave ground-truth simulator. We also use source and ground-truth normalization with an evolving replay dataset to stabilize and accelerate learning. Using this approach, we train a fast, single-step surrogate for two-dimensional wave scattering with up to 41,772 controllable variables, including dense, freely configurable grids of refractive indices and complex-valued sources. The resulting neural surrogate is robustly accurate across diverse structured and unstructured examples and generalizes inductively to larger domains, reaching over 3 million controllable variables without retraining, a $73.8\times$ increase. We demonstrate the surrogate on large-scale forward simulations and inverse design of freeform beam splitters and gradient-index (GRIN) lenses up to 98 wavelengths wide, showing comparable or better performance than FDTD-based designs, with speedups from $1.29\times$ to $26.5\times$. These results demonstrate a practical path toward fast, robustly accurate, inductively scalable neural simulators for photonic inverse design and other wave-scattering inverse problems.
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