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Abstract This article proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient method of dynamics learning and system identification. First, a low-level model is trained to learn the system dynamics, which utilizes multiple simple neural networks to approximate the local dynamics generated from data-driven partitions. Then, based on the low-level model, a high-level model is trained to abstract the low-level neural hybrid system model into a transition system that allows computational tree logic (CTL) verification to promote model’s ability to handle human interaction and verification efficiency. 

In this paper, a data-driven neural hybrid system modeling framework via the Maximum Entropy partitioning approach is proposed for complex dynamical system modeling such as human motion dynamics. The sampled data collected from the system is partitioned into segmented data sets using the Maximum Entropy approach, and the mode transition logic is then defined. Then, as the local dynamical description for their corresponding partitions, a collection of small-scale neural networks is trained. Following a neural hybrid system model of the system, a set-valued reachability analysis with low computation cost is provided based on interval analysis and a split and combined process to demonstrate the benefits of our approach in computationally expensive tasks. Finally, a numerical examples of the limit cycle and a human behavior modeling example are provided to demonstrate the effectiveness and efficiency of the developed methods. 

In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions into groups corresponding to their topologies and based on which, transition guards are defined. Then, a collection of small-scale neural networks that are computationally efficient are trained as the local dynamical description for their corresponding topologies. After modeling the system with a neural-network-based hybrid automaton, the set-valued reachability analysis with low computation cost is provided based on interval analysis and a split and combined process. At last, a numerical example of the limit cycle is presented to illustrate that the developed models can significantly reduce the computational cost in reachable set computation without sacrificing any modeling precision.