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<p>AUTO, a software package specifically designed to analyze continuation and bifurcation in differential equations, enables a deeper understanding of the behavior of solutions across varying parameters in complex dynamical systems. A common approach to deriving traveling pulse solutions of the FitzHugh-Nagumo (FHN) equation is to employ AUTO to systematically track these solutions and explore their stability as key parameters change. However, the solutions generated often exhibit highly irregular data, prompting this study to introduce a cutting-edge deep learning strategy aimed at their regularization. Within this deep learning framework, we employ a modified Levenberg-Marquardt optimization algorithm to enhance the analysis and understanding of complex dynamical systems. This approach not only refines the regularity of traveling pulse solutions but also extends its applicability beyond neuronal dynamics, providing a robust solution for a wide range of problems characterized by irregular data.</p>

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Deep Learning-Enhanced Regularization of Irregular Traveling Pulses in the FitzHugh-Nagumo Model

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Burhan Bezekci

摘要

AUTO, a software package specifically designed to analyze continuation and bifurcation in differential equations, enables a deeper understanding of the behavior of solutions across varying parameters in complex dynamical systems. A common approach to deriving traveling pulse solutions of the FitzHugh-Nagumo (FHN) equation is to employ AUTO to systematically track these solutions and explore their stability as key parameters change. However, the solutions generated often exhibit highly irregular data, prompting this study to introduce a cutting-edge deep learning strategy aimed at their regularization. Within this deep learning framework, we employ a modified Levenberg-Marquardt optimization algorithm to enhance the analysis and understanding of complex dynamical systems. This approach not only refines the regularity of traveling pulse solutions but also extends its applicability beyond neuronal dynamics, providing a robust solution for a wide range of problems characterized by irregular data.