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Geometric Neural Ordinary Differential Equations: From Manifolds to Lie Groups [PDF]
EntropyNeural ordinary differential equations (neural ODEs) are a well-established tool for optimizing the parameters of dynamical systems, with applications in image classification, optimal control, and physics learning.
Yannik P. Wotte +2 more
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Noise-aware training of neuromorphic dynamic device networks [PDF]
Nature CommunicationsIn materio computing offers the potential for widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction.
Luca Manneschi +16 more
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Complexities of differentiable dynamical systems [PDF]
Journal of Mathematical Physics, 2020 We define the notion of localizable property for a dynamical system. Then, we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the number of periodic points, the positive entropy, and the high emergence.
Pierre Berger
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Classical Fisher information for differentiable dynamical systems
Chaos, 2023 Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty.
Mohamed Sahbani +2 more
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Sampled-Data Consensus for Networked Euler-Lagrange Systems With Differentiable Scaling Functions
IEEE Access, 2021 This paper is concerned with the sampled-data consensus of networked Euler-Lagrange systems. The Euler-Lagrange system has enormous advantages in analyzing and designing dynamical systems.
Yilin Wang +3 more
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Differentiability of the Largest Lyapunov Exponent for Non-Planar Open Billiards
Mathematics, 2023 This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system.
Amal Al Dowais
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On differentially dissipative dynamical systems [PDF]
IFAC Proceedings Volumes, 2013 Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability.
Fulvio Forni, Rodolphe Sepulchre
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Landau: A Language for Dynamical Systems with Automatic Differentiation [PDF]
Journal of Mathematical Sciences, 2020 Most numerical solvers used to determine free variables of dynamical systems rely on first-order derivatives of the state of the system w.r.t. the free variables. The number of the free variables can be fairly large. One of the approaches of obtaining those derivatives is the integration of the derivatives simultaneously with the dynamical equations ...
Ivan Dolgakov, Dmitry Pavlov
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A Mean-Field Game Control for Large-Scale Swarm Formation Flight in Dense Environments
Sensors, 2022 As an important part of cyberphysical systems (CPSs), multiple aerial drone systems are widely used in various scenarios, and research scenarios are becoming increasingly complex.
Guofang Wang +3 more
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Numerical Modeling Tools and S-derivatives
Моделирование и анализ информационных систем, 2022 Numerical study of various processes leads to the need of clarification (extensions) of the limits of applicability of computational constructs and modeling tools.
Anatoly Nikolaevich Morozov
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