Identification of Dynamical Systems using Symbolic Regression

• URL: http://arxiv.org/abs/2107.06131v1
• Date: Tue, 6 Jul 2021 11:41:10 GMT
• Title: Identification of Dynamical Systems using Symbolic Regression
• Authors: Gabriel Kronberger, Lukas Kammerer, Michael Kommenda
• Abstract summary: We describe a method for the identification of models for dynamical systems from observational data. The novelty is that we add a step of gradient-based optimization of the ODE parameters. We find that gradient-based optimization of parameters improves predictive accuracy of the models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential equations (ODE). The novelty is that we add a step of gradient-based optimization of the ODE parameters. For this we calculate the sensitivities of the solution to the initial value problem (IVP) using automatic differentiation. The proposed approach is tested on a set of 19 problem instances taken from the literature which includes datasets from simulated systems as well as datasets captured from mechanical systems. We find that gradient-based optimization of parameters improves predictive accuracy of the models. The best results are obtained when we first fit the individual equations to the numeric differences and then subsequently fine-tune the identified parameter values by fitting the IVP solution to the observed variable values.

Related papers

• Automating the Discovery of Partial Differential Equations in Dynamical Systems [0.0]
  We present an extension to the ARGOS framework, ARGOS-RAL, which leverages sparse regression with the recurrent adaptive lasso to identify PDEs automatically. We rigorously evaluate the performance of ARGOS-RAL in identifying canonical PDEs under various noise levels and sample sizes. Our results show that ARGOS-RAL effectively and reliably identifies the underlying PDEs from data, outperforming the sequential threshold ridge regression method in most cases.
  arXiv  Detail & Related papers  (2024-04-25T09:23:03Z)
• Robust identification of non-autonomous dynamical systems using stochastic dynamics models [0.0]
  This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model. We show that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID.
  arXiv  Detail & Related papers  (2022-12-20T16:36:23Z)
• Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
  Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations. We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
  arXiv  Detail & Related papers  (2022-10-15T17:32:49Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations [2.741266294612776]
  We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE) PI-VAE consists of a variational autoencoder (VAE), which generates samples of system variables and parameters. The satisfactory accuracy and efficiency of the proposed method are numerically demonstrated in comparison with physics-informed generative adversarial network (PI-WGAN)
  arXiv  Detail & Related papers  (2022-03-21T21:51:19Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• 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)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Numerical Solution of Stiff Ordinary Differential Equations with Random Projection Neural Networks [0.0]
  We propose a numerical scheme based on Random Projection Neural Networks (RPNN) for the solution of Ordinary Differential Equations (ODEs) We show that our proposed scheme yields good numerical approximation accuracy without being affected by the stiffness, thus outperforming in same cases the textttode45 and textttode15s functions.
  arXiv  Detail & Related papers  (2021-08-03T15:49:17Z)
• Meta-Solver for Neural Ordinary Differential Equations [77.8918415523446]
  We investigate how the variability in solvers' space can improve neural ODEs performance. We show that the right choice of solver parameterization can significantly affect neural ODEs models in terms of robustness to adversarial attacks.
  arXiv  Detail & Related papers  (2021-03-15T17:26:34Z)
• Non-intrusive surrogate modeling for parametrized time-dependent PDEs using convolutional autoencoders [0.0]
  We present a non-intrusive surrogate modeling scheme based on machine learning for predictive modeling of complex, systems by parametrized timedependent PDEs. We use a convolutional autoencoder in conjunction with a feed forward neural network to establish a low-cost and accurate mapping from problem's parametric space to its solution space.
  arXiv  Detail & Related papers  (2021-01-14T11:34:58Z)

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.