Extraction of Discrete Spectra Modes from Video Data Using a Deep Convolutional Koopman Network

• URL: http://arxiv.org/abs/2010.09245v1
• Date: Mon, 19 Oct 2020 06:26:29 GMT
• Title: Extraction of Discrete Spectra Modes from Video Data Using a Deep Convolutional Koopman Network
• Authors: Scott Leask, Vincent McDonell
• Abstract summary: Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems. Deep Koopman networks attempt to learn the Koopman eigenfunctions which capture the coordinate transformation to globally linearize system dynamics. We demonstrate the ability of a deep convolutional Koopman network (CKN) in automatically identifying independent modes for dynamical systems with discrete spectra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions which capture the coordinate transformation to globally linearize system dynamics. These eigenfunctions can be linked to underlying system modes which govern the dynamical behavior of the system. While many related techniques have demonstrated their efficacy on canonical systems and their associated state variables, in this work the system dynamics are observed optically (i.e. in video format). We demonstrate the ability of a deep convolutional Koopman network (CKN) in automatically identifying independent modes for dynamical systems with discrete spectra. Practically, this affords flexibility in system data collection as the data are easily obtainable observable variables. The learned models are able to successfully and robustly identify the underlying modes governing the system, even with a redundantly large embedding space. Modal disaggregation is encouraged using a simple masking procedure. All of the systems analyzed in this work use an identical network architecture.

Related papers

• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Learning dynamical systems: an example from open quantum system dynamics [0.0]
  We will study the dynamics of a small spin chain coupled with dephasing gates. We show how Koopman operator learning is an approach to efficiently learn not only the evolution of the density matrix, but also of every physical observable associated to the system.
  arXiv  Detail & Related papers  (2022-11-12T14:36:13Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Dynamic Inference with Neural Interpreters [72.90231306252007]
  We present Neural Interpreters, an architecture that factorizes inference in a self-attention network as a system of modules. inputs to the model are routed through a sequence of functions in a way that is end-to-end learned. We show that Neural Interpreters perform on par with the vision transformer using fewer parameters, while being transferrable to a new task in a sample efficient manner.
  arXiv  Detail & Related papers  (2021-10-12T23:22:45Z)
• 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)
• Deep Learning Enhanced Dynamic Mode Decomposition [0.0]
  We use convolutional autoencoder networks to simultaneously find optimal families of observables. We also generate both accurate embeddings of the flow into a space of observables and immersions of the observables back into flow coordinates. This network results in a global transformation of the flow and affords future state prediction via EDMD and the decoder network.
  arXiv  Detail & Related papers  (2021-08-10T03:54:23Z)
• Discovering Sparse Interpretable Dynamics from Partial Observations [0.0]
  We propose a machine learning framework for discovering these governing equations using only partial observations. Our tests show that this method can successfully reconstruct the full system state.
  arXiv  Detail & Related papers  (2021-07-22T18:23:23Z)
• CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels [5.286010070038216]
  We present a convolutional neural network (CNN) based on the Koopman operator (CKNet) to identify the latent dynamics from raw pixels. Experiments show that identified dynamics with 32-dim can predict validly 120 steps and generate clear images.
  arXiv  Detail & Related papers  (2021-02-19T23:29:08Z)
• Applications of Koopman Mode Analysis to Neural Networks [52.77024349608834]
  We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. We show how the Koopman spectrum can be used to determine the number of layers required for the architecture. We also show how using Koopman modes we can selectively prune the network to speed up the training procedure.
  arXiv  Detail & Related papers  (2020-06-21T11:00:04Z)
• Learning Stable Deep Dynamics Models [91.90131512825504]
  We propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics.
  arXiv  Detail & Related papers  (2020-01-17T00:04:45Z)

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.