# A Data-Driven Hybrid Automaton Framework to Modeling Complex Dynamical Systems

arXiv: https://arxiv.org/abs/2304.13811 · HTML: https://mlsanity.com/paper/2304.13811/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 26 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach](https://mlsanity.com/paper/2004.12273/) (2020)
- [Artificial neural network as a universal model of nonlinear dynamical systems](https://mlsanity.com/paper/2104.05402/) (2021)
- [Learnability and Robustness of Shallow Neural Networks Learned With a Performance-Driven BP and a Variant PSO For Edge Decision-Making](https://mlsanity.com/paper/2008.06135/) (2020)
- [Robust Optimization Framework for Training Shallow Neural Networks Using Reachability Method](https://mlsanity.com/paper/2107.12801/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Transition System Abstraction Framework for Neural Network Dynamical System Models](https://mlsanity.com/paper/2402.11739/) (2024)

## Abstract (arXiv)

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.