Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning

• URL: http://arxiv.org/abs/2209.06910v1
• Date: Wed, 7 Sep 2022 12:27:11 GMT
• Title: Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning
• Authors: K.H. Lee and D.A.W. Barton and L.Renson
• Abstract summary: We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. A data-driven mapping from this model to the experimental observations is then identified based on experimental data using machine learning techniques. The method is shown to be general, data-efficient and to offer good accuracy without any prior knowledge about the system other than its bifurcation structure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential equation normal-form model capturing the bifurcation structure of the system. A data-driven mapping from this model to the experimental observations is then identified based on experimental data using machine learning techniques. The proposed method is first demonstrated numerically on a Van der Pol oscillator and a three-degree-of-freedom aeroelastic model. It is then applied to model the behaviour of a physical aeroelastic structure exhibiting limit cycle oscillations during wind tunnel tests. The method is shown to be general, data-efficient and to offer good accuracy without any prior knowledge about the system other than its bifurcation structure.

Related papers

• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Equivariant Graph Neural Operator for Modeling 3D Dynamics [148.98826858078556]
  We propose Equivariant Graph Neural Operator (EGNO) to directly models dynamics as trajectories instead of just next-step prediction. EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods.
  arXiv  Detail & Related papers  (2024-01-19T21:50:32Z)
• 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)
• Differentiable physics-enabled closure modeling for Burgers' turbulence [0.0]
  We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models.
  arXiv  Detail & Related papers  (2022-09-23T14:38:01Z)
• 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)
• Identification of high order closure terms from fully kinetic simulations using machine learning [0.0]
  We show how two different machine learning models can synthesize higher-order moments extracted from a kinetic simulation. The accuracy of the models and their ability to generalize are evaluated and compared to a baseline model. We learn that both models can capture heat flux and pressure tensor very well, with the gradient boosting regressor being the most stable of the two models.
  arXiv  Detail & Related papers  (2021-10-19T12:27:02Z)
• 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)
• Generative Temporal Difference Learning for Infinite-Horizon Prediction [101.59882753763888]
  We introduce the $gamma$-model, a predictive model of environment dynamics with an infinite probabilistic horizon. We discuss how its training reflects an inescapable tradeoff between training-time and testing-time compounding errors.
  arXiv  Detail & Related papers  (2020-10-27T17:54:12Z)
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics [3.214927790437842]
  Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
  arXiv  Detail & Related papers  (2020-05-29T15:10:43Z)

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.