Building Hybrid B-Spline And Neural Network Operators

• URL: http://arxiv.org/abs/2406.06611v1
• Date: Thu, 6 Jun 2024 21:54:59 GMT
• Title: Building Hybrid B-Spline And Neural Network Operators
• Authors: Raffaele Romagnoli, Jasmine Ratchford, Mark H. Klein,
• Abstract summary: Control systems are indispensable for ensuring the safety of cyber-physical systems (CPS) We propose a novel strategy that combines the inductive bias of B-splines with data-driven neural networks to facilitate real-time predictions of CPS behavior.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Control systems are indispensable for ensuring the safety of cyber-physical systems (CPS), spanning various domains such as automobiles, airplanes, and missiles. Safeguarding CPS necessitates runtime methodologies that continuously monitor safety-critical conditions and respond in a verifiably safe manner. A fundamental aspect of many safety approaches involves predicting the future behavior of systems. However, achieving this requires accurate models that can operate in real time. Motivated by DeepONets, we propose a novel strategy that combines the inductive bias of B-splines with data-driven neural networks to facilitate real-time predictions of CPS behavior. We introduce our hybrid B-spline neural operator, establishing its capability as a universal approximator and providing rigorous bounds on the approximation error. These findings are applicable to a broad class of nonlinear autonomous systems and are validated through experimentation on a controlled 6-degree-of-freedom (DOF) quadrotor with a 12 dimensional state space. Furthermore, we conduct a comparative analysis of different network architectures, specifically fully connected networks (FCNN) and recurrent neural networks (RNN), to elucidate the practical utility and trade-offs associated with each architecture in real-world scenarios.

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