AI 中文总结
针对偏微分方程控制物理系统逆设计难题，NOTES集成降维、表示学习与进化优化，结合神经算子与CMA-ES在紧凑潜在空间全局优化，在纳米光子束偏转器及结构优化中表现出色，提供了灵活可转移的逆设计框架。
AI 中文摘要
由偏微分方程控制的物理系统的逆设计，因其设计空间的高维度和非凸性而在计算上要求很高。逆设计的生成模型往往缺乏鲁棒性和可转移性，而进化策略虽然鲁棒，但在高维空间中存在困难。本文介绍了一种神经算子驱动的拓扑信息进化策略（NOTES），它集成了降维、表示学习和进化优化，以实现高效且可转移的逆设计。NOTES将基于DeepONet的神经算子与协方差矩阵自适应进化策略（CMA-ES）相结合，在一个紧凑的潜在空间中进行全局优化，该空间编码拓扑感知先验，同时为未见操作条件发现高性能设计。应用于由麦克斯韦方程控制的纳米光子束偏转器逆设计时，NOTES将设计维度从256降至25，并始终实现超过95%的效率，优于CMA-ES拓扑优化和其他基线。应用于结构优化时，NOTES发现了合规性低至246的设计。通过在偏微分方程求解器中解耦DeepONet的拓扑学习与控制物理，NOTES为物理系统的逆设计提供了一个灵活且可转移的框架。
英文摘要
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.
