Reachable Set Estimation and Verification for Neural Network Models of Nonlinear Dynamic Systems

Xiang, Weiming; Lopez, Diego Manzanas; Musau, Patrick; Johnson, Taylor T.

doi:10.1007/978-3-319-97301-2_7

by Weiming Xiang, Diego Manzanas Lopez, Patrick Musau, Taylor T. Johnson

Abstract:

Neural networks have been widely used to solve complex real-world problems. Due to the complex, nonlinear, non-convex nature of neural networks, formal safety and robustness guarantees for the behaviors of neural network systems are crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and safety verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural networks involved in the model are a class of feed-forward neural networks called Multi-Layer Perceptrons (MLPs). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation of each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of the reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of non-empty intersections between unsafe regions and the estimated reachable set. Several numerical examples are provided to illustrate the approach.

Reference:

Weiming Xiang, Diego Manzanas Lopez, Patrick Musau, Taylor T. Johnson, "Reachable Set Estimation and Verification for Neural Network Models of Nonlinear Dynamic Systems", In (Huafeng Yu, Xin Li, Richard M. Murray, S. Ramesh, Claire J. Tomlin, eds.), Springer International Publishing, pp. 123–144, 2019.

Bibtex Entry:

@article{xiang2019ust,
author="Xiang, Weiming
and Lopez, Diego Manzanas
and Musau, Patrick
and Taylor T. Johnson",
editor="Yu, Huafeng
and Li, Xin
and Murray, Richard M.
and Ramesh, S.
and Tomlin, Claire J.",
title="Reachable Set Estimation and Verification for Neural Network Models of Nonlinear Dynamic Systems",
bookTitle="Safe, Autonomous and Intelligent Vehicles",
year="2019",
publisher="Springer International Publishing",
pages="123--144",
abstract="Neural networks have been widely used to solve complex real-world problems. Due to the complex, nonlinear, non-convex nature of neural networks, formal safety and robustness guarantees for the behaviors of neural network systems are crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and safety verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural networks involved in the model are a class of feed-forward neural networks called Multi-Layer Perceptrons (MLPs). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation of each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of the reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of non-empty intersections between unsafe regions and the estimated reachable set. Several numerical examples are provided to illustrate the approach.",
isbn="978-3-319-97301-2",
doi="10.1007/978-3-319-97301-2_7",
pdf = {http://www.taylortjohnson.com/research/xiang2018ust.pdf},
}