Computationally efficient neural hybrid automaton framework for learning complex dynamics

This paper proposes a computationally efficient and effective data-driven modeling framework for dynamical systems. The proposed modeling framework employs a collection of shallow neural networks known as Extreme Learning Machines (ELMs) to model local system behaviors along with data-driven inferred transitions among local models to establish a neural hybrid automaton model. First, the sampled system inputs are mapped to the corresponding feature spaces to obtain data-driven partitions, which subsequently define the transitions and invariants of the neural hybrid automaton model through a novel data-driven mode clustering process. Then, a collection of ELMs are trained to approximate the local dynamics. The learning processes integrate a segmented data merging procedure for location identification and a local dynamics modeling process. The proposed neural hybrid automaton models can capture behaviors of complex dynamical systems with high modeling precision but significantly lower computational complexities in computationally expensive tasks such as training and verification, which are traditionally considered to be computationally expensive tasks for neural network models. A computationally efficient set-valued reachability analysis method which is commonly used in safety verification is then developed based on interval analysis and a novel Split and Combine process. Finally, applications to modeling the limit cycle and human handwritten motions are presented to show the effectiveness and efficiency of our approach.