Building Hybrid B-Spline And Neural Network Operators

TL;DR

This paper introduces a hybrid B-spline neural operator for real-time prediction of cyber-physical system behavior, combining inductive bias with data-driven models, validated on a quadrotor system.

Contribution

It proposes a novel hybrid B-spline neural operator with theoretical approximation bounds, applicable to nonlinear autonomous systems, and compares neural network architectures for practical use.

Findings

The hybrid operator acts as a universal approximator with error bounds.

Validated on a 6-DOF quadrotor with 12-dimensional state space.

Compared FCNN and RNN architectures for real-world utility.

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.