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Learning Theory for Dynamical Systems
SIAM Journal on Applied Dynamical Systems, 2023 The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then explicitly learning the dynamics from this information.
Tyrus Berry, Suddhasattwa Das
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Mathematics, 2021 This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations is also analyzed ...
Narciso Román-Roy
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Physical Review Research, 2022 Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics.
Naoki Masuda, Prosenjit Kundu
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Dark Type Dynamical Systems: The Integrability Algorithm and Applications
Algorithms, 2022 Based on a devised gradient-holonomic integrability testing algorithm, we analyze a class of dark type nonlinear dynamical systems on spatially one-dimensional functional manifolds possessing hidden symmetry properties and allowing their linearization on
Yarema A. Prykarpatsky +3 more
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Time-averaging axion-like interacting scalar fields models
European Physical Journal C: Particles and Fields, 2021 In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless
Saikat Chakraborty +3 more
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On the birth of limit cycles for non-smooth dynamical systems [PDF]
, 2014 The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems.
Andronov +31 more
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Data-driven prediction in dynamical systems: recent developments
Philosophical Transactions of the Royal Society A, 2022 In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems
Amin Ghadami, B. Epureanu
semanticscholar +1 more source
Stack- and Queue-like Dynamics in Recurrent Neural Networks [PDF]
, 2005 What dynamics do simple recurrent networks (SRNs) develop to represent stack-like and queue-like memories? SRNs have been widely used as models in cognitive science.
Bennell, Julia A., Song, Xiang
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Double field theory at SL(2) angles
Journal of High Energy Physics, 2017 An extended field theory is presented that captures the full SL(2) × O(6, 6 + n) duality group of four-dimensional half-maximal supergravities. The theory has section constraints whose two inequivalent solutions correspond to minimal D = 10 supergravity ...
Franz Ciceri +4 more
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Synchronization of dissipative dynamical systems driven by non-Gaussian Lévy noises [PDF]
, 2009 Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation, and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties.
Duan, Jinqiao +3 more
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