Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems

• URL: http://arxiv.org/abs/2109.00538v1
• Date: Wed, 1 Sep 2021 16:29:21 GMT
• Title: Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems
• Authors: Shailesh Garg and Souvik Chakraborty and Budhaditya Hazra
• Abstract summary: For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. We propose a novel gray-box modeling approach that not only identifies the model-form error but also utilizes it to improve the predictive capability of the known but approximate governing equation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduced model-form error into the system. In this paper, we propose a novel gray-box modeling approach that not only identifies the model-form error but also utilizes it to improve the predictive capability of the known but approximate governing equation. The primary idea is to treat the unknown model-form error as a residual force and estimate it using duel Bayesian filter based joint input-state estimation algorithms. For improving the predictive capability of the underlying physics, we first use machine learning algorithm to learn a mapping between the estimated state and the input (model-form error) and then introduce it into the governing equation as an additional term. This helps in improving the predictive capability of the governing physics and allows the model to generalize to unseen environment. Although in theory, any machine learning algorithm can be used within the proposed framework, we use Gaussian process in this work. To test the performance of proposed framework, case studies discussing four different dynamical systems are discussed; results for which indicate that the framework is applicable to a wide variety of systems and can produce reliable estimates of original system's states.

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Koopman-based Deep Learning for Nonlinear System Estimation [1.3791394805787949]
  We present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.
  arXiv  Detail & Related papers  (2024-05-01T16:49:54Z)
• LEARNEST: LEARNing Enhanced Model-based State ESTimation for Robots using Knowledge-based Neural Ordinary Differential Equations [4.3403382998035624]
  In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms. To enhance the dynamics models and improve the estimation accuracy, we utilize a deep learning framework known as knowledge-based neural ordinary differential equations (KNODEs) In our proposed LEARNEST framework, we integrate the data-driven model into two novel model-based state estimation algorithms, which are denoted as KNODE-MHE and KNODE-UKF.
  arXiv  Detail & Related papers  (2022-09-16T22:16:40Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• A Framework for Machine Learning of Model Error in Dynamical Systems [7.384376731453594]
  We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems from data. We cast the problem in both continuous- and discrete-time, for problems in which the model error is memoryless and in which it has significant memory. We find that hybrid methods substantially outperform solely data-driven approaches in terms of data hunger, demands for model complexity, and overall predictive performance.
  arXiv  Detail & Related papers  (2021-07-14T12:47:48Z)
• 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)
• Identification of Probability weighted ARX models with arbitrary domains [75.91002178647165]
  PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX) The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field.
  arXiv  Detail & Related papers  (2020-09-29T12:50:33Z)
• Bayesian differential programming for robust systems identification under uncertainty [14.169588600819546]
  This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers. The use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics.
  arXiv  Detail & Related papers  (2020-04-15T00:51:14Z)

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.