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

• URL: http://arxiv.org/abs/2304.13811v1
• Date: Wed, 26 Apr 2023 20:18:12 GMT
• Title: A Data-Driven Hybrid Automaton Framework to Modeling Complex Dynamical Systems
• Authors: Yejiang Yang, Zihao Mo, Weiming Xiang
• Abstract summary: A data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors. Small-scale neural networks are trained as the local dynamical description for their corresponding topologies. 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.
• Score: 2.610470075814367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Model-Based Control with Sparse Neural Dynamics [23.961218902837807]
  We propose a new framework for integrated model learning and predictive control. We show that our framework can deliver better closed-loop performance than existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-12-20T06:25:02Z)
• Iterative self-transfer learning: A general methodology for response time-history prediction based on small dataset [0.0]
  An iterative self-transfer learningmethod for training neural networks based on small datasets is proposed in this study. The results show that the proposed method can improve the model performance by near an order of magnitude on small datasets.
  arXiv  Detail & Related papers  (2023-06-14T18:48:04Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Analyzing Populations of Neural Networks via Dynamical Model Embedding [10.455447557943463]
  A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an algorithm that constructs low-dimensional manifold where each point corresponds to a neural network model, and two points are nearby if the corresponding neural networks enact similar high-level computational processes. DYNAMO takes as input a collection of pre-trained neural networks and outputs a meta-model that emulates the dynamics of the hidden states as well as the outputs of any model in the collection.
  arXiv  Detail & Related papers  (2023-02-27T19:00:05Z)
• Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression [2.7071541526963805]
  This paper proposes a novel neural network-based symbolic regression method. It constructs physically plausible models based on even very small training data sets and prior knowledge about the system. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system.
  arXiv  Detail & Related papers  (2023-02-01T22:05:04Z)
• An advanced spatio-temporal convolutional recurrent neural network for storm surge predictions [73.4962254843935]
  We study the capability of artificial neural network models to emulate storm surge based on the storm track/size/intensity history. This study presents a neural network model that can predict storm surge, informed by a database of synthetic storm simulations.
  arXiv  Detail & Related papers  (2022-04-18T23:42:18Z)
• Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning [50.24174211654775]
  We present a novel contrastive self-supervised learning framework for anomaly detection on attributed networks. Our framework fully exploits the local information from network data by sampling a novel type of contrastive instance pair. A graph neural network-based contrastive learning model is proposed to learn informative embedding from high-dimensional attributes and local structure.
  arXiv  Detail & Related papers  (2021-02-27T03:17:20Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Learning Queuing Networks by Recurrent Neural Networks [0.0]
  We propose a machine-learning approach to derive performance models from data. We exploit a deterministic approximation of their average dynamics in terms of a compact system of ordinary differential equations. This allows for an interpretable structure of the neural network, which can be trained from system measurements to yield a white-box parameterized model.
  arXiv  Detail & Related papers  (2020-02-25T10:56:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.