Ray tracing through the crystalline lens of the eye is a complex optical problem traditionally tackled by mathematical techniques that may lack optimal accuracy. This paper introduces a novel method that integrates the Grey Wolf optimizer (GWO) with an artificial neural network (ANN), termed ANNGWO, to enhance the precision of ray tracing through the lens. The ANNGWO approach involves defining a cost function with a multi-layer neural network incorporating three activation functions: Log-sigmoid, Radial basis, and Tan-sigmoid. GWO is then employed to optimize this cost function, effectively simulating the intricate geometry of the crystalline lens. The methodology includes designing a multi-layer ANN with the activation function to model the ray tracing problem.This is followed by constructing the cost function by formulating the unsupervised error function for the equation and its initial conditions. Subsequently, GWO is utilized to minimize this cost function, thereby enhancing the accuracy of the simulation. The performance of ANNGWO is compared with traditional methods, including the Laplace decomposition method (LDM), multi-step differential transform method (MDTM), and the fourth-order Runge–Kutta method (RKM). Numerical experiments demonstrate that ANNGWO significantly improves accuracy. For instance, the mean absolute error (AE) using the Log-sigmoid activation function is 6.869×10−2 for 10 neurons. Best-case AE values range from 3.390×10−4 to 1.169×10−2, outperforming traditional methods. Additionally, ANNGWO exhibits consistently lower standard deviation of absolute error across all time steps, reflecting enhanced stability. Compared to LDM, MDTM, and RKM, ANNGWO achieves a significant reduction in error, underscoring its superior precision and reliability. The method’s ability to avoid local minima and its robust convergence behavior make it a powerful tool for simulating light movement in the eye, with promising applications in vision research and ocular imaging.

中文翻译：

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使用人工神经网络和 Grey Wolf 优化器通过眼睛的晶状体进行光线追踪的问题优化


通过眼睛的晶状体进行光线追踪是一个复杂的光学问题，传统上由数学技术解决，可能缺乏最佳精度。本文介绍了一种将 Grey Wolf 优化器 （GWO） 与人工神经网络 （ANN） 集成在一起的新方法，称为 ANNGWO，以提高通过镜头进行光线追踪的精度。ANNGWO 方法涉及使用多层神经网络定义成本函数，该网络包含三个激活函数：对数 sigmoid、径向基和 Tan-sigmoid。然后，使用 GWO 来优化此成本函数，从而有效地模拟晶体透镜的复杂几何形状。该方法包括设计一个具有激活函数的多层 ANN，以对光线追踪问题进行建模。然后通过为方程及其初始条件制定无监督误差函数来构造成本函数。随后，利用 GWO 来最小化这个成本函数，从而提高模拟的准确性。将 ANNGWO 的性能与传统方法进行了比较，包括拉普拉斯分解法 （LDM）、多步微分变换法 （MDTM） 和四阶龙格-库塔法 （RKM）。数值实验表明，ANNGWO 显著提高了准确性。例如，对于 10 个神经元，使用 Log-sigmoid 激活函数的平均绝对误差 （AE） 为 6.869×10−2。最佳情况下的 AE 值范围为 3.390×10−4 至 1.169×10−2，优于传统方法。此外，ANNGWO 在所有时间步长中都表现出始终较低的绝对误差标准差，反映了增强的稳定性。与 LDM、MDTM 和 RKM 相比，ANNGWO 实现了显著的误差减少，凸显了其卓越的精度和可靠性。 该方法能够避免局部最小值及其强大的会聚行为，使其成为模拟眼睛中光线运动的强大工具，在视觉研究和眼部成像中具有广阔的应用前景。