Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems

Simulating electromagnetic wave scattering is central to photonics and computational imaging, but traditional full-wave solvers like finite-difference time-domain (FDTD) are computationally prohibitive for iterative inverse design tasks that require millions of evaluations. Nonrecurrent, single-step neural network surrogates offer orders-of-magnitude speedups but have traditionally been limited to just a few tens of variables due to the exponential growth of training data requirements. This paper investigates whether an active, data-driven training strategy can overcome this scaling bottleneck.

The authors propose a dynamic training framework that runs in parallel with surrogate training. Instead of relying on random sampling or fixed datasets, a hard-example generator uses gradient ascent to actively search for refractive-index and complex-valued source configurations that maximize the disagreement between the current surrogate and an FDTD ground-truth solver. To stabilize learning and prevent catastrophic feedback loops, these generated examples are stored in an evolving replay buffer, and both predictions and errors are normalized by the root-mean-square amplitude of the ground-truth fields to manage near-resonant high-energy configurations.

The dynamic training approach dramatically outperforms random sampling, yielding significantly lower validation loss and high physical fidelity across diverse structured and unstructured scattering problems. The resulting U-Net-based neural surrogate is successfully trained on 64x64 and 128x128 domains containing up to 41,772 controllable variables. Furthermore, because the architecture is fully convolutional, the trained model exhibits strong inductive scalability: it generalizes without retraining to larger domains of 1024x1024 pixels—reaching over 3 million controllable variables (a 73.8x increase).

When applied to downstream inverse design workloads—such as freeform beam splitters and gradient-index (GRIN) lenses up to 98 wavelengths wide—the surrogate achieves comparable or superior performance to traditional FDTD-based designs while providing end-to-end optimization speedups ranging from 1.29x to 26.5x.