物理信息神经网络解偏微分方程设计渐进镜片  

Designing Progressive Lenses Using Physics-Informed Neural Networks to Solve Partial Differential Equations

作　　者：项华中[1,2] 程慧 丁琦慧 郑泽希 陈家璧[4] 王成[1,2] 张大伟[4] 庄松林[4] Xiang Huazhong;Cheng Hui;Ding Qihui;Zheng Zexi;Chen Jiabi;Wang Cheng;Zhang Dawei;Zhuang Songlin(Institute of Medical Optics and Optometry,School of Health Science and Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;Shanghai Engineering Research Center of Interventional Medical Device,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Optical-Electrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学健康科学与工程学院医学光学与视光学研究所,上海200093 [2]上海理工大学上海介入医疗器械工程技术研究中心,上海200093 [3]上海理工大学机械工程学院,上海200093 [4]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《光学学报》2025年第1期218-228,共11页Acta Optica Sinica

基　　金：国家自然科学基金(61605114,52206102)。

摘　　要：提出一种基于物理信息神经网络(PINN)求解非线性偏微分方程设计渐进多焦点镜片的方法。使用显式有限差分算法生成训练数据,建立深度卷积神经网络模型,构建量化偏微分方程残差的损失函数,同时约束施加边界条件后的残差,在迭代过程中最小化损失函数来更新神经网络参数(权重和偏置)并输出优化后的镜片面形。最后,通过数值法和PINN设计并加工6组镜片。结果表明:经PINN设计的3组镜片,远用区的光焦度误差更小,在0.05 D(1 D=l m^(-1))以内;远近用区像散也更小,仅0.02 D;加光度与理论值之间的误差显著降低,最小误差为0.1 D。所提方法在优化镜片光学性能的同时,远近用区域面积和宽度等参数基本没有变化,达到了优化要求。所提出的PINN方法为渐进多焦点镜片的优化提供了一种新的方法。Objective The design of freeform progressive addition lenses is to provide wearers with a seamless transition between distance and near vision.As human lifespan increases and digital lifestyles become more prevalent,progressive lenses have become an essential visual aid.Although research on progressive lenses in China has advanced and design techniques have become more sophisticated,existing design methods still have certain limitations.For example,the computation of sagittal height is resource-intensive,with high time costs and limited precision.These limitations can cause the addition power to fail to meet expected standards,reduce the effective visual area,and make wearers feel uncomfortable when switching between distance and near vision.This,in turn,increases the visual adaptation time and may prevent the initial lens design from fully achieving its intended purpose.The goal of our study is to explore a more efficient and precise solution by proposing a method based on physics-informed neural network(PINN)for solving nonlinear partial differential equations and applying it to optimize the design of progressive addition lenses.Traditional numerical methods for solving nonlinear partial differential equations often face challenges such as high computational complexity and slow convergence rates.This innovative computational model optimizes the sagittal height distribution by minimizing the error between the neural network output and the governing equations,breaks the limitations of dimensionality,avoids truncation errors and numerical integration errors of variational forms,and overcomes the constraints of traditional design methods.This enables precise simulation of the sagittal height of progressive addition lenses,thereby improving lens optical performance and enhancing user visual experience.Methods We describe the theoretical foundation of the partial differential equations(PDEs)guiding the design of progressive addition lenses and propose a method for solving the PDEs of progressive addition lenses using

关 键 词：物理信息神经网络 自由曲面 渐进多焦点镜片 像散 光焦度 

分 类 号：TH74[机械工程—光学工程]