• Corpus ID: 238744007

Extracting Dynamical Models from Data

  title={Extracting Dynamical Models from Data},
  author={Michael F. Zimmer},
  • M. Zimmer
  • Published 13 October 2021
  • Computer Science
  • ArXiv
The FJet approach is introduced for determining the underlying model of a dynamical system. It borrows ideas from the fields of Lie symmetries as applied to differential equations (DEs), and numerical integration (such as Runge-Kutta). The technique can be considered as a way to use machine learning (ML) to derive a numerical integration scheme. The technique naturally overcomes the "extrapolation problem", which is when ML is used to extrapolate a model beyond the time range of the original… 


Equations of Motion from a Data Series
A method to reconstruct the deterministic portion of the equations of motion directly from a data series to represent a vast reduction of a chaotic data set’s observed complexity to a compact, algorithmic specification is described.
Data-driven discovery of partial differential equations
The sparse regression method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation.
Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning
The proposed DeLaN network can learn the equations of motion of a mechanical system with a deep network efficiently while ensuring physical plausibility and exhibits substantially improved and more robust extrapolation to novel trajectories and learns online in real-time.
Reconstruction of vector fields: The case of the Lorenz system.
  • Gouesbet
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
This paper is devoted to the case of the Lorenz system, where ordinary differential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series.
Machine-Learning Non-Conservative Dynamics for New-Physics Detection
The Neural New-Physics Detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and non-conservative components, which are represented by a Lagrangian Neural Network and a universal approximator network, respectively.
Poincaré, celestial mechanics, dynamical-systems theory and “chaos”
Abstract As demonstrated by the success of James Gleick's recent book [1987], there is considerable interest in the scientific community and among the general public in “chaos” and the “new science”
Nonlinear prediction of chaotic time series
Numerical techniques are presented for constructing nonlinear predictive models directly from time series data and scaling laws are developed which describe the data requirements for reliable predictions.
Reconstructing equations of motion from experimental data with unobserved variables.
  • Breeden, Hübler
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1990
A method for reconstructing equations of motion for systems where all the necessary variables have not been observed is developed, which can be applied to systems with one or several hidden variables, and can be used to reconstruct maps or differential equations.
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
In the words of the authors, the goal of this book was to “bring together many of the important new ideas in learning, and explain them in a statistical framework.” The authors have been quite
A magnetoelastic strange attractor
Abstract Experimental evidence is presented for chaotic type non-periodic motions of a deterministic magnetoelastic oscillator. These motions are analogous to solutions in non-linear dynamic systems