A Bridge between Dynamical Systems and Machine Learning: Engineered
  Ordinary Differential Equations as Classification Algorithm (EODECA)
Raffaele Marino Lorenzo Giambagli Lorenzo Chicchi Lorenzo Buffoni Duccio Fanelli
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.