Learning strange attractors with reservoir systems

• URL: http://arxiv.org/abs/2108.05024v1
• Date: Wed, 11 Aug 2021 04:29:18 GMT
• Title: Learning strange attractors with reservoir systems
• Authors: Lyudmila Grigoryeva, Allen Hart, and Juan-Pablo Ortega
• Abstract summary: This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement. It provides additional tools for the representation, learning, and analysis of chaotic attractors.
• Score: 8.201100713224003
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.

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)
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance [49.1574468325115]
  We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. We find that the dynamics of the spin ensemble now spans a more expansive effective Hilbert space.
  arXiv  Detail & Related papers  (2023-09-19T16:44:14Z)
• Autoencoders for discovering manifold dimension and coordinates in data from complex dynamical systems [0.0]
  Autoencoder framework combines implicit regularization with internal linear layers and $L$ regularization (weight decay) We show that this framework can be naturally extended for applications of state-space modeling and forecasting.
  arXiv  Detail & Related papers  (2023-05-01T21:14:47Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
  We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
  arXiv  Detail & Related papers  (2022-07-14T10:05:20Z)
• Inferring the Structure of Ordinary Differential Equations [12.202646598683888]
  We extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available.
  arXiv  Detail & Related papers  (2021-07-05T07:55:05Z)
• Embedding Information onto a Dynamical System [0.0]
  We show how an arbitrary sequence can be mapped into another space as an attractive solution of a nonautonomous dynamical system. This result is not a generalization of Takens embedding theorem but helps us understand what exactly is required by discrete-time state space models.
  arXiv  Detail & Related papers  (2021-05-22T16:54:16Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Dissipative Deep Neural Dynamical Systems [0.9864260997723973]
  We leverage the representation of neural networks as pointwise affine maps to expose their local linear operators. This allows us to "crack open the black box" of the neural dynamical system's behavior. We analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.
  arXiv  Detail & Related papers  (2020-11-26T23:13:16Z)
• Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations [33.63818978256567]
  We present LG-ODE, a latent ordinary differential equation generative model for modeling multi-agent dynamic system with known graph structure. It can simultaneously learn the embedding of high dimensional trajectories and infer continuous latent system dynamics. Our model employs a novel encoder parameterized by a graph neural network that can infer initial states in an unsupervised way.
  arXiv  Detail & Related papers  (2020-11-08T01:02:22Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

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.