基于深度物理启发神经网络的微波波导器件逆设计方法

刘金品; 王秉中; 陈传升; 王任

doi:10.7498/aps.72.20230031

摘要

使用物理启发的神经网络方法求解物理逆问题正成为一种趋势, 但仅通过损失函数引入物理信息的方案难以求解. 为解决电磁器件逆设计中物理启发神经网络模型不易收敛的问题, 本文引出了深度物理启发神经网络. 深度物理启发神经网络使用偏微分方程的基本解构成的网络替代传统的前馈神经网络, 将数学物理模型嵌入网络结构. 这一特点使深度物理启发网络的训练参数具有实际物理意义, 相较传统物理启发神经网络拥有更简洁的损失函数, 计算效率和稳定性也有明显提升. 以二端口波导的散射参数设计为例, 数值实验结果表明该方案在保证与设计目标相关性系数大于0.99的同时, 最快可在25 s实现器件逆设计, 且能够获得多样化的结构设计结果. 本文提出的方法为逆物理问题求解构建及神经网络的物理信息嵌入探索提供了新思路.

关键词:

Abstract

Using physics-informed neural networks to solve physical inverse problems is becoming a trend. However, it is difficult to solve the scheme that only introduces physical knowledge through the loss function. Constructing a reasonable loss function to make the results converge becomes a challenge. To address the challenge of physics-informed neural network models for inverse design of electromagnetic devices, a deep physics-informed neural network is introduced by using the mode matching method. The physical equations have been integrated into the network structure when the network is constructed. This feature makes the deep physics-informed neural network have a more concise loss function and higher computational efficiency when solving physical inverse problems. In addition, the training parameters of deep physics-informed neural networks are physically meaningful compared with those of traditional physics-informed neural networks. Users can control the network by parameters more easily. Taking the scattering parameter design of a two-port waveguide for example, we present a new metal topology inverse design scheme and give a detailed explanation. In numerical experiments, we target a set of physically realizable scattering parameters and inversely design the metallic septum by using a deep physics-informed neural network. The results show that the method can not only achieve the design target but also obtain solutions with different topologies. The establishment of multiple solutions is extremely valuable in implementing the inverse design. It can allow the designer to determine the size and location of the design area more freely while achieving the performance requirements. This scheme is expected to promote the application and development of the inverse design of electromagnetic devices.

Keywords:

作者及机构信息

电子科技大学应用物理研究所, 成都　611731

通信作者: 王秉中, bzwang@uestc.edu.cn ; 王任, rwang@uestc.edu.cn

基金项目: 国家自然科学基金(批准号: 62171081, 61901086)、四川省自然科学基金(批准号: 2022NSFSC0039)和四川省科技计划项目(批准号: 2021YJ0100)资助的课题.

Authors and contacts

Institute of Applied Physics, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Wang Bing-Zhong, bzwang@uestc.edu.cn ; Wang Ren, rwang@uestc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62171081, 61901086), the Natural Science Foundation of Sichuan Province, China (Grant No. 2022NSFSC0039), and the Science and Technology Planning Project of Sichuan Province, China (Grant No. 2021YJ0100).

文章全文 : translate this paragraph

参考文献

[1]	Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt-Maranto L, Zdeborová L 2019 Rev. Mod. Phys. 91 045002 Google Scholar
[2]	Kim B, Lee S, Kim J 2020 Sci. Adv. 6 eaax9324 Google Scholar
[3]	Li L, Wang L G, Teixeira F L, Liu C, Nehorai A, Cui T J 2018 IEEE Trans. Antennas Propag. 67 1819 Google Scholar
[4]	Yang R, Xu X, Li X, Wang L, Pu F 2020 IGARSS 2020-2020 IEEE International Geoscience and Remote Sensing Symposium Waikoloa, HI, USA, September 26–October 2, 2020 pp1743–1746
[5]	Shen C, Krenn M, Eppel S, Aspuru-Guzik A 2021 Mach. Learn. -Sci. Technol. 2 03LT02 Google Scholar
[6]	Gebauer N W, Gastegger M, Hessmann S S, Müller K R, Schütt K T 2022 Nat. Commun. 13 973 Google Scholar
[7]	Xu X, Sun C, Li Y, Zhao J, Han J, Huang W 2021 Opt. Commun. 481 126513 Google Scholar
[8]	Liu Z, Zhu D, Rodrigues S, P, Lee K, T, Cai W 2018 Nano Lett. 18 6570 Google Scholar
[9]	Kudyshev Z A, Kildishev A V, Shalaev V M, Boltasseva A 2020 Appl. Phys. Rev. 7 021407 Google Scholar
[10]	Song Q, Xu F, Zhu X X, Jin Y Q 2021 IEEE Trans. Geosci. Remote Sensing 60 1 Google Scholar
[11]	Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686 Google Scholar
[12]	Cai S, Wang Z, Wang S, Perdikaris P, Karniadakis G E 2021 J. Heat Transfer 143 060801 Google Scholar
[13]	Mao Z, Jagtap A D, Karniadakis G E 2020 Comput. Meth. Appl. Mech. Eng. 360 112789 Google Scholar
[14]	Khan A, Lowther D A 2022 IEEE Trans. Magn. 58 1 Google Scholar
[15]	Chen Y, Dal Negro L 2022 APL Photonics 7 010802 Google Scholar
[16]	Wang S, Teng Y, Perdikaris P 2021 SIAM J. Sci. Comput. 43 A3055 Google Scholar
[17]	Lu L, Pestourie R, Yao W, Wang Z, Verdugo F, Johnson S G 2021 SIAM J. Sci. Comput. 43 B1105 Google Scholar
[18]	Rohrhofer F M, Posch S, Geiger B C 2021 arXiv Preprint arXiv: 2105.00862
[19]	Yu J, Lu L, Meng X, Karniadakis G E 2022 Comput. Meth. Appl. Mech. Eng. 393 114823 Google Scholar
[20]	Daw A, Bu J, Wang S, Perdikaris P, Karpatne A 2022 arXiv Preprint arXiv: 2207.02338
[21]	Peng W, Zhou W, Zhang X, Yao W, Liu Z 2022 arXiv Preprint arXiv: 2205.01051
[22]	Hu Y, Jin Y, Wu X, Chen J 2021 IEEE Trans. Antennas Propag. 70 767 Google Scholar
[23]	Leroy M 1983 IEEE Trans. Antennas Propag. 31 655 Google Scholar

施引文献

图 1 二端口波导结构示意图　(a) 逆设计模型 ; (b) 设计目标参数获取模型

Fig. 1. Schematic diagram of the two-port waveguide structure: (a) Inverse design model; (b) the model used to obtain the target parameters.

下载: 全尺寸图片幻灯片

图 2 传统PINN模型

Fig. 2. Traditional PINN model.

下载: 全尺寸图片幻灯片

图 3 MPINN模型

Fig. 3. MPINN model.

下载: 全尺寸图片幻灯片

图 4 DPINN模型

Fig. 4. DPINN model.

下载: 全尺寸图片幻灯片

图 5 四频点二端口矩形波导逆设计结果　(a) $g\left( x \right)$ 分布与二值化结果; (b) 损失函数误差与优化迭代次数关系; (c) 数值仿真测得散射参数

Fig. 5. Inverse design results of two-port rectangular waveguide targeted at four frequency points: (a) The output $g\left( x \right)$ of the network and its binarization result; (b) the relationship between the loss function error and the number of optimization iterations; (c) scattering parameters measured by the numerical simulation.

下载: 全尺寸图片幻灯片

图 6 同一目标下DPINN逆设计的多种不同膜片结构　(a) PEC膜片结构示意图; (b) 数值仿真测得散射参数

Fig. 6. Different structures obtained using DPINN under the same target: (a) Schematic diagram of PEC septum with different structures; (b) scattering parameters measured by numerical simulation.

下载: 全尺寸图片幻灯片

图 7 二维膜片逆设计　(a) 设计目标参数获取模型尺寸示意图; (b) DPINN输出$ \tilde g(x, y) $; (c) 二值化后结构尺寸示意图; (d) 数值仿真测得散射参数幅度; (e) 数值仿真测得散射参数实部及虚部

Fig. 7. Inverse design of two-dimensional iris: (a) Schematic diagram of model size for obtaining design target parameters; (b) $\tilde g(x, y)$ of the DPINN output; (c) structural dimension diagram after binarization; (d) the amplitudes of the scattering parameters measured by numerical simulation; (e) the real and imaginary parts of the scattering parameters measured by numerical simulation.

下载: 全尺寸图片幻灯片

表 1 逆设计目标S参数

Table 1. Target S parameter of inverse design.

参数项	4 GHz	5 GHz	6 GHz	7 GHz
S₂₁实部	0.34244	0.20439	–0.55995	–0.88062
S₂₁虚部	0.11409	–0.65687	–0.59222	0.07926

下载: 导出CSV

表 2 网络模型详细参数

Table 2. Detailed parameters of neural network model.

项目		传统PINN	MPINN	DPINN
优化器		Adam	Adam	Adam
网络实现	$ \tilde g(x) $	FNN: 3×20	FNN: 3×20	FNN: 3×20
网络实现	其余	FNN: 3×20	(5)式和(6)式M = 100	(12)式M = 100
损失函数		$ {L_{{\text{PINN}}}} $	$ {L_{{\text{design}}}} $	$ {L_{{\text{DPINN}}}} $
采样点		Evo采样^[20]	完全随机	完全随机
迭代次数		2×10⁵	2×10⁵	2×10⁵
学习率		10^–3	10^–3	10^–3

下载: 导出CSV

[1]	Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt-Maranto L, Zdeborová L 2019 Rev. Mod. Phys. 91 045002 Google Scholar
[2]	Kim B, Lee S, Kim J 2020 Sci. Adv. 6 eaax9324 Google Scholar
[3]	Li L, Wang L G, Teixeira F L, Liu C, Nehorai A, Cui T J 2018 IEEE Trans. Antennas Propag. 67 1819 Google Scholar
[4]	Yang R, Xu X, Li X, Wang L, Pu F 2020 IGARSS 2020-2020 IEEE International Geoscience and Remote Sensing Symposium Waikoloa, HI, USA, September 26–October 2, 2020 pp1743–1746
[5]	Shen C, Krenn M, Eppel S, Aspuru-Guzik A 2021 Mach. Learn. -Sci. Technol. 2 03LT02 Google Scholar
[6]	Gebauer N W, Gastegger M, Hessmann S S, Müller K R, Schütt K T 2022 Nat. Commun. 13 973 Google Scholar
[7]	Xu X, Sun C, Li Y, Zhao J, Han J, Huang W 2021 Opt. Commun. 481 126513 Google Scholar
[8]	Liu Z, Zhu D, Rodrigues S, P, Lee K, T, Cai W 2018 Nano Lett. 18 6570 Google Scholar
[9]	Kudyshev Z A, Kildishev A V, Shalaev V M, Boltasseva A 2020 Appl. Phys. Rev. 7 021407 Google Scholar
[10]	Song Q, Xu F, Zhu X X, Jin Y Q 2021 IEEE Trans. Geosci. Remote Sensing 60 1 Google Scholar
[11]	Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686 Google Scholar
[12]	Cai S, Wang Z, Wang S, Perdikaris P, Karniadakis G E 2021 J. Heat Transfer 143 060801 Google Scholar
[13]	Mao Z, Jagtap A D, Karniadakis G E 2020 Comput. Meth. Appl. Mech. Eng. 360 112789 Google Scholar
[14]	Khan A, Lowther D A 2022 IEEE Trans. Magn. 58 1 Google Scholar
[15]	Chen Y, Dal Negro L 2022 APL Photonics 7 010802 Google Scholar
[16]	Wang S, Teng Y, Perdikaris P 2021 SIAM J. Sci. Comput. 43 A3055 Google Scholar
[17]	Lu L, Pestourie R, Yao W, Wang Z, Verdugo F, Johnson S G 2021 SIAM J. Sci. Comput. 43 B1105 Google Scholar
[18]	Rohrhofer F M, Posch S, Geiger B C 2021 arXiv Preprint arXiv: 2105.00862
[19]	Yu J, Lu L, Meng X, Karniadakis G E 2022 Comput. Meth. Appl. Mech. Eng. 393 114823 Google Scholar
[20]	Daw A, Bu J, Wang S, Perdikaris P, Karpatne A 2022 arXiv Preprint arXiv: 2207.02338
[21]	Peng W, Zhou W, Zhang X, Yao W, Liu Z 2022 arXiv Preprint arXiv: 2205.01051
[22]	Hu Y, Jin Y, Wu X, Chen J 2021 IEEE Trans. Antennas Propag. 70 767 Google Scholar
[23]	Leroy M 1983 IEEE Trans. Antennas Propag. 31 655 Google Scholar

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