Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds

• URL: http://arxiv.org/abs/2201.04976v1
• Date: Thu, 13 Jan 2022 13:21:55 GMT
• Title: Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
• Authors: Mattia Cenedese, Joar Ax{\aa}s, Bastian B\"auerlein, Kerstin Avila and George Haller
• Abstract summary: We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing.

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)
• Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders [0.0]
  We introduce a class of nonlinear projections described by constrained autoencoder neural networks in which both the manifold and the projection fibers are learned from data. Our architecture uses invertible activation functions and biorthogonal weight matrices to ensure that the encoder is a left inverse of the decoder. We also introduce new dynamics-aware cost functions that promote learning of oblique projection fibers that account for fast dynamics and nonnormality.
  arXiv  Detail & Related papers  (2023-07-28T04:01:48Z)
• 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)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Nonlinear proper orthogonal decomposition for convection-dominated flows [0.0]
  We propose an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.
  arXiv  Detail & Related papers  (2021-10-15T18:05:34Z)
• Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems [1.7499351967216341]
  We review a data-driven nonlinear model reduction methodology based on spectral submanifolds (SSMs) As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low dimensional invariants. These normal forms capture amplitude-dependent properties and are accurate enough to provide predictions for non-linearizable system response under the additions of external forcing.
  arXiv  Detail & Related papers  (2021-10-05T10:39:40Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• Hessian Eigenspectra of More Realistic Nonlinear Models [73.31363313577941]
  We make a emphprecise characterization of the Hessian eigenspectra for a broad family of nonlinear models. Our analysis takes a step forward to identify the origin of many striking features observed in more complex machine learning models.
  arXiv  Detail & Related papers  (2021-03-02T06:59:52Z)
• Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics [49.41640137945938]
  We propose a neural dynamic mode decomposition for estimating a lift function based on neural networks. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
  arXiv  Detail & Related papers  (2020-12-11T08:34:26Z)
• Coarse-Grained Nonlinear System Identification [0.0]
  We introduce Coarse-Grained Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. We demonstrate the properties of this approach on a simple synthetic problem. We also demonstrate this approach experimentally, showing that it identifies an accurate model of the nonlinear voltage to dynamics of a tungsten filament with less than a second of experimental data.
  arXiv  Detail & Related papers  (2020-10-14T06:45:51Z)
• Latent variable modeling with random features [7.856578780790166]
  We develop a family of nonlinear dimension reduction models that are easily to non-Gaussian data likelihoods. Our generalized RFLVMs produce results comparable with other state-of-the-art dimension reduction methods.
  arXiv  Detail & Related papers  (2020-06-19T14:12:05Z)

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.