Physically Analyzable AI-Based Nonlinear Platoon Dynamics Modeling During Traffic Oscillation: A Koopman Approach
- URL: http://arxiv.org/abs/2406.14696v1
- Date: Thu, 20 Jun 2024 19:35:21 GMT
- Title: Physically Analyzable AI-Based Nonlinear Platoon Dynamics Modeling During Traffic Oscillation: A Koopman Approach
- Authors: Kexin Tian, Haotian Shi, Yang Zhou, Sixu Li,
- Abstract summary: There exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability.
This paper proposes an AI-based Koopman approach to model the unknown nonlinear platoon dynamics harnessing the power of AI.
- Score: 4.379212829795889
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there are two predominant approaches: the physics model-based approach and the Artificial Intelligence (AI)--based approach. Knowing the facts that the physical-based model usually lacks sufficient modeling accuracy and potential function mismatches and the pure-AI-based method lacks analyzability, this paper innovatively proposes an AI-based Koopman approach to model the unknown nonlinear platoon dynamics harnessing the power of AI and simultaneously maintain physical analyzability, with a particular focus on periods of traffic oscillation. Specifically, this research first employs a deep learning framework to generate the embedding function that lifts the original space into the embedding space. Given the embedding space descriptiveness, the platoon dynamics can be expressed as a linear dynamical system founded by the Koopman theory. Based on that, the routine of linear dynamical system analysis can be conducted on the learned traffic linear dynamics in the embedding space. By that, the physical interpretability and analyzability of model-based methods with the heightened precision inherent in data-driven approaches can be synergized. Comparative experiments have been conducted with existing modeling approaches, which suggests our method's superiority in accuracy. Additionally, a phase plane analysis is performed, further evidencing our approach's effectiveness in replicating the complex dynamic patterns. Moreover, the proposed methodology is proven to feature the capability of analyzing the stability, attesting to the physical analyzability.
Related papers
- eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling [9.52474299688276]
We introduce a low-rank structured variational autoencoder framework for nonlinear state-space graphical models.
We show that our approach consistently demonstrates the ability to learn a more predictive generative model.
arXiv Detail & Related papers (2024-03-03T02:19:49Z) - Discovering Interpretable Physical Models using Symbolic Regression and
Discrete Exterior Calculus [55.2480439325792]
We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models.
DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems.
We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
arXiv Detail & Related papers (2023-10-10T13:23:05Z) - 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) - Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying
Non-Autonomous Dynamical Systems [0.0]
We propose a physics-guided hybrid approach for modeling non-autonomous systems under control.
This is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy.
Experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.
arXiv Detail & Related papers (2022-04-27T14:33:02Z) - Gradient-Based Trajectory Optimization With Learned Dynamics [80.41791191022139]
We use machine learning techniques to learn a differentiable dynamics model of the system from data.
We show that a neural network can model highly nonlinear behaviors accurately for large time horizons.
In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car.
arXiv Detail & Related papers (2022-04-09T22:07:34Z) - Learning continuous models for continuous physics [94.42705784823997]
We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications.
Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
arXiv Detail & Related papers (2022-02-17T07:56:46Z) - Constructing Neural Network-Based Models for Simulating Dynamical
Systems [59.0861954179401]
Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system.
This paper provides a survey of the different ways to construct models of dynamical systems using neural networks.
In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
arXiv Detail & Related papers (2021-11-02T10:51:42Z) - Using scientific machine learning for experimental bifurcation analysis
of dynamic systems [2.204918347869259]
This study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles.
We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments.
We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach.
arXiv Detail & Related papers (2021-10-22T15:43:03Z) - Physics-guided Deep Markov Models for Learning Nonlinear Dynamical
Systems with Uncertainty [6.151348127802708]
We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM)
The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
arXiv Detail & Related papers (2021-10-16T16:35:12Z) - Learning Unstable Dynamics with One Minute of Data: A
Differentiation-based Gaussian Process Approach [47.045588297201434]
We show how to exploit the differentiability of Gaussian processes to create a state-dependent linearized approximation of the true continuous dynamics.
We validate our approach by iteratively learning the system dynamics of an unstable system such as a 9-D segway.
arXiv Detail & Related papers (2021-03-08T05:08:47Z)
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.