In a world increasingly reliant on machine learning, the interpretability of these models remains a substantial challenge, with many equating their functionality to an enigmatic black box. This study seeks to bridge machine learning and dynamical systems. Recognizing the deep parallels between dense neural networks and dynamical systems, particularly in the light of non-linearities and successive transformations, this manuscript introduces the Engineered Ordinary Differential Equations as Classification Algorithms (EODECAs). Uniquely designed as neural networks underpinned by continuous ordinary differential equations, EODECAs aim to capitalize on the well-established toolkit of dynamical systems. Unlike traditional deep learning models, which often suffer from opacity, EODECAs promise both high classification performance and intrinsic interpretability. They are naturally invertible, granting them an edge in understanding and transparency over their counterparts. By bridging these domains, we hope to usher in a new era of machine learning models where genuine comprehension of data processes complements predictive prowess.

翻译：在机器学习日益普及的当今世界，模型的可解释性仍是重大挑战，许多人将其功能等同于神秘的黑箱。本研究旨在弥合机器学习与动力系统之间的鸿沟。鉴于深度神经网络与动力系统在非线性变换及逐层转化方面存在深刻相似性，本文提出工程化常微分方程分类算法（EODECA）。该算法创新性地构建在连续常微分方程驱动的神经网络框架之上，旨在充分利用动力系统的成熟分析工具。与常因不透明性而受限的传统深度学习模型不同，EODECA兼具高分类性能与内在可解释性。其天然可逆的特性使其在模型理解与透明度方面优于同类模型。通过连接这两个领域，我们期待开启机器学习的新纪元，在预测能力之外，重拾对数据过程的深层理解。