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

   https://doi.org/10.1109/ICIT58465.2023.10143031  

   Yang, Yejiang; Mo, Zihao; Xiang, Weiming (April 2023, 2023 IEEE International Conference on Industrial Technology (ICIT))

   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. 

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2. Designing Hybrid Neural Network Using Physical Neurons—A Case Study of Drill Bit-Rock Interaction Modeling

   https://doi.org/10.1115/1.4062631  

   Zhang, Zihang; Song, Xingyong (September 2023, Journal of Dynamic Systems, Measurement, and Control)

   Abstract Neural networks have been widely applied in system dynamics modeling. One particular type of networks, hybrid neural networks, combines a neural network model with a physical model, which can increase rate of convergence in training. However, most existing hybrid neural network methods require an explicit physical model constructed, which sometimes might not be feasible in practice or could weaken the capability of capturing complex and hidden physical phenomena. In this paper, we propose a novel approach to construct a hybrid neural network. The new method incorporates the physical information to the structure of network construction, but does not need an explicit physical model constructed. The method is then applied to modeling of bit-rock interaction in the down-hole drilling system as a case study, to demonstrate its effectiveness in modeling complex process and efficiency of convergence in training. 

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3. Efficient Neural Hybrid System Learning and Interpretable Transition System Abstraction for Dynamical Systems

   https://doi.org/10.1115/1.4066516  

   Yang, Yejiang; Mo, Zihao; Xiang, Weiming (January 2025, ASME Letters in Dynamic Systems and Control)

   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. 

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4. Data-driven model discovery and model selection for noisy biological systems

   https://doi.org/10.1371/journal.pcbi.1012762  

   Wu, Xiaojun; McDermott, MeiLu; MacLean, Adam L (January 2025, PLOS Computational Biology)

   Alber, Mark (Ed.)

   Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. Machine learning methods offer alternative means of model construction: differential equation models can be learnt from data via model discovery using sparse identification of nonlinear dynamics (SINDy). However, SINDy struggles with realistic levels of biological noise and is limited in its ability to incorporate prior knowledge of the system. We propose a data-driven framework for model discovery and model selection using hybrid dynamical systems: partial models containing missing terms. Neural networks are used to approximate the unknown dynamics of a system, enabling the denoising of the data while simultaneously learning the latent dynamics. Simulations from the fitted neural network are then used to infer models using sparse regression. We show, via model selection, that model discovery using hybrid dynamical systems outperforms alternative approaches. We find it possible to infer models correctly up to high levels of biological noise of different types. We demonstrate the potential to learn models from sparse, noisy data in application to a canonical cell state transition using data derived from single-cell transcriptomics. Overall, this approach provides a practical framework for model discovery in biology in cases where data are noisy and sparse, of particular utility when the underlying biological mechanisms are partially but incompletely known. 

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5. Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllers

   Jafarpour, Saber; Harapanahalli, Akash; Coogan, Samuel (June 2023, 5th Annual Learning for Dynamics & Control Conference)

   N. Matni, M. Morari (Ed.)

   This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing verification algorithm to construct inclusion functions for its input-output behavior. Inspired by mixed monotone theory, we embed the closed-loop dynamics into a larger system using an inclusion function of the neural network and a decomposition function of the open-loop system. This embedding provides a scalable approach for safety analysis of the neural control loop while preserving the nonlinear structure of the system. We show that one can efficiently compute hyper-rectangular over-approximations of the reachable sets using a single trajectory of the embedding system. We design an algorithm to leverage this computational advantage through partitioning strategies, improving our reachable set estimates while balancing its runtime with tunable parameters. We demonstrate the performance of this algorithm through two case studies. First, we demonstrate this method’s strength in complex nonlinear environments. Then, we show that our approach matches the performance of the state-of-the art verification algorithm for linear discretized systems. 

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