Hybrid Method for Inverse Design of Orbital Angular Momentum Transmission Fiber Based on Neural Network and Optimization Algorithms

Qin, Haibo; Huang, Wei; Song, Binbin; Chen, Shengyong

doi:10.1109/jlt.2022.3185059

Cited by 11 publications

(1 citation statement)

References 24 publications

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“…On the other hand, DNNs boast remarkable flexibility and data-driven learning capabilities [4] [5], yet suffer from the main challenge of immense training times and inadequacy of literature surrounding their desirable numerical properties such as stability, convergence, etc, that are highly valuable to engineers and mathematicians. Therefore through developing hybrids of FEM and DNNs, numerous works have sought to reconcile the challenges of both FEM and DNNs [6], [7], [8], [1], [9], [10], [11]. The FEM has been extensively studied for decades, serving as a cornerstone for solving PDEs [?…”

Section: Introductionmentioning

confidence: 99%

Characterizing Parameter Equivalence and Approximation in 1D FEM and ReLU NNs

Katende,

Oleynik,

Kasumba

et al. 2024

Preprint

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This paper introduces a novel methodology for characterizing parameter equivalence between Rectified Linear Unit (ReLU) Neural Networks (NNs) and 1D Finite Element Models (FEMs). By expressing the FEM solution equation in terms of neural networks and employing a hybrid scheme involving partially trained nested neural networks, we bridge the gap between these two computational paradigms. Our approach offers a promising avenue to leverage the flexibility of neural networks while retaining the established principles of FEM. Through extensive numerical experiments, we demonstrate the efficacy of our scheme in function interpolation and solving partial differential equations (PDEs). In function interpolation tasks, our hybrid scheme consistently outperforms fully trainable ReLU NNs, achieving significantly lower error factors across various scenarios. Similarly, in solving PDEs, our approach exhibits superior accuracy compared to fully trainable ReLU NNs, as evidenced by lower L2-error factors. We further extend the application of our hybrid scheme to diverse PDEs including the heat, Poisson, and wave equations, showcasing its versatility and effectiveness across different problem domains. This work not only presents a significant advancement in computational methods but also lays the groundwork for redefining the FEM algorithm within an algorithmic framework. These findings have implications for a wide range of scientific and engineering disciplines, and we believe they warrant consideration for publication in high-impact journals.

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