Results 21 to 30 of about 94,059 (356)

On some dynamical reconstruction problems for a nonlinear system of the second-order [PDF]

Opuscula Mathematica, 2010
The problem of reconstruction of unknown characteristics of a nonlinear system is considered. Solution algorithms stable with respect to the informational noise and computational errors are specified. These algorithms are based on the method of auxiliary
Marina Blizorukova, Vyacheslav Maksimov
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An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games, 2021
This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are
Alexander Arguchintsev, Vasilisa Poplevko   +1 more
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Stiff neural ordinary differential equations [PDF]

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021
Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems.
Suyong Kim, Weiqi Ji, Sili Deng, Yingbo Ma, Christopher Rackauckas   +4 more
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ON SINGULAR SOLUTIONS OF CLAIRAUT EQUATIONS IN THE THEORY OF ORDINARY DIFFERENTIAL AND PARTIAL DERIVATIVE EQUATIONS

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. There is no problem in finding a general solution to the ordinary differential Clairaut equation. The corresponding procedure is described in details in the theory of ordinary differential equations.
L. A. Zhidova
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A method for constructing a complete bifurcation picture of a boundary value problem for nonlinear partial differential equations: application of the Kolmogorov-Arnold theorem [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика
The purpose of this study is to develop a numerical method for bifurcation analysis of nonlinear partial differential equations, based on the reduction of partial differential equations to ordinary ones, using the Kolmogorov-Arnold theorem.
Gromov, Vasily Alexandrovich, Tomashchuk, Korney Kirillovich, Beschastnov, Yury Nikolaevich, Sidorenko, Artem Aleksandrovich, Kakurin, Vasily Vladimirovich   +4 more
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Optical neural ordinary differential equations

Optics Letters, 2023
Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successive cascading of network hidden layers results in larger integrated photonic chip areas. To address this issue, we propose the optical neural ordinary differential equations (ON-ODEs) architecture that parameterizes ...
Yun Zhao, Hang Chen, Min Lin, Haiou Zhang, Tao Yan, Xing Lin, Ruqi Huang, Qionghai Dai   +7 more
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Predicting Ordinary Differential Equations with Transformers

CoRR, 2023
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in extensive empirical evaluations that our model performs better or on par with existing methods in terms of accurate ...
Becker, S., Klein, M., Neitz, A., Parascandolo, G., Kilbertus, N.   +4 more
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Characteristic Neural Ordinary Differential Equations

CoRR, 2021
We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an ODE, C-NODE models the evolution of the latent variables as the solution of a family of first-order quasi-linear ...
Xingzi Xu, Ali Hasan, Khalil Elkhalil, Jie Ding 0002, Vahid Tarokh   +4 more
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Neural Ordinary Differential Equations

CoRR, 2018
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver.
Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, David Duvenaud   +3 more
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Solving Ordinary Differential Equations with Discontinuities [PDF]

ACM Transactions on Mathematical Software, 1984
Automatic codes for differential equations can be inadequate when the solutions have discontinuities. If the user provides an external indicator for discontinuities (e.g., a switching function whose sign changes indicate discontinuities), a code can be more efficient.
Gear, C. W., Østerby, Ole
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