基于扩散模型的高阶拓扑绝缘体实时设计

REAL-TIME DESIGN OF HIGHER-ORDER TOPOLOGICAL INSULATORS BY DIFFUSION MODEL

作为一种全新的波控工具,高阶拓扑绝缘体可以将能量鲁棒高效地局域化在低维空间,且对缺陷不敏感.在光子和声子系统中,高阶拓扑绝缘体的快速设计仍然是一项挑战.采用移动可变形孔洞法显式描述C4v对称的单胞构型,并结合能带理论和对称指标刻画其性能(拓扑性质和非平凡带隙宽度).在此基础上,构建了包含几何参数、无量纲化带隙宽度与拓扑性质指标的高阶拓扑绝缘体数据集,并提出了一种基于去噪扩散概率模型(denoising diffusion probabilistic model,DDPM)的实时设计框架.相比采用其他生成式模型的设计框架,DDPM有效避免了训练不稳定和生成保真度低等问题.该框架可以精准且快速地按目标需求或最大化带隙宽度逆向设计力学高阶拓扑绝缘体,在单机上生成所需设计的平均相对误差在3.5%以内,平均耗时仅需0.01 s,相比传统逆向设计方法效率提升6~7个数量级.通过使用Wasserstein距离度量逆向设计样本的多样性,该框架相较基于深度学习代理模型的优化设计结果,表现出更高的生成结果多样性.此外,所得设计具有显式描述的几何信息,可以直接与CAD/CAE软件结合,避免了隐式描述算法中的后处理步骤.这种基于DDPM的实时设计框架可扩展应用于多物理场拓扑材料和其他类型超材料的逆向设计,并为构建声子和光子拓扑材料的数据库提供了基础.

As a novel tool for wave manipulation,higher-order topological insulators can efficiently and robustly localize energy in low-dimensional space,exhibiting insensitivity to defects.Nevertheless,the fast design of higher-order topological insulators in photonic and phononic systems is still a challenge.In the present work,C4v-symmetric continuum unit cells are explicitly described by the moving morphable voids method,and the concerned properties(topological properties and non-trivial bandgap width)are measured by the band theory and symmetry indicators.Based upon these,a dataset of higher-order topological insulators is constructed,incorporating geometric parameters,normalized bandgap width,and topological property indicators.A real-time design paradigm is proposed utilizing a denoising diffusion probabilistic model(DDPM).Compared to design paradigms using other generative models,DDPM effectively avoids issues such as training instability and low fidelity in generation.This paradigm enables accurately and fast inverse design of mechanical higher-order topological insulators based on target requirements or maximizing the non-trivial bandgap width.Applying this developed inverse design paradigm,the average relative error for generating the desired designs on a desktop computer is within 3.5%,with an average generation time of only 0.01 seconds,which significantly improves the design efficiency by 6 to 7 orders of magnitude compared with the traditional inverse design methods.By using the Wasserstein distance to measure the diversity of inverse design results,this paradigm exhibits higher diversity compared to the optimization design results obtained by deep learning based surrogate model.In addition,the generated designs have explicitly described geometric information,so they can be directly integrated with CAD/CAE software,avoiding the post-processing step required in implicit description methods.This real-time design paradigm based on DDPM can be easily extended to inverse design of multi-physical topological materials and other types of metamaterials,laying the foundation for constructing databases for photonic and phononic topological materials.