Building Hybrid B-Spline And Neural Network Operators
<|reference_start|>Building Hybrid B-Spline And Neural Network Operators: 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.<|reference_end|>
@article{romagnoli2024building,
    title={Building Hybrid B-Spline And Neural Network Operators},
    author={Raffaele Romagnoli, Jasmine Ratchford, Mark H. Klein},
    journal={arXiv preprint arXiv:2406.06611},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06611},
    primaryClass={cs.LG cs.AI cs.SY eess.SY}
}