Integrating continuous-time neural networks in engineering: bridging machine learning and dynamical system modeling

Abstract

This paper examines the integration of Continuous-Time Neural Networks (CTNNs), including Neural ODEs, CDEs, Neural Laplace, and Neural Flows, into engineering practices, particularly in dynamical system modeling. We provide a detailed introduction to CTNNs, highlighting their underutilization in engineering despite similarities with traditional Ordinary Differential Equation (ODE) models. Through a comparative analysis with conventional engineering approaches, using a spring-mass-damper system as an example, we demonstrate both theoretical and practical aspects of CTNNs in engineering contexts. Our work underscores the potential of CTNNs to harmonize with traditional engineering methods, exploring their applications in Cyber- Physical Systems (CPS). Additionally, we review key open-source software tools for implementing CTNNs, aiming to facilitate their broader integration into engineering practices.