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Kernel Ordinary Differential Equations. [PDF]
J Am Stat Assoc, 2022 Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow ...
Dai X, Li L.
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On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations [PDF]
Opuscula Mathematica, 2021 We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group.
Ivan Tsyfra
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Ordinary Differential Equations [PDF]
, 2021 AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem.
Christian Seifert +2 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 +4 more
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Mendel, 2022 This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti +2 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 +7 more
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Solving Ordinary Differential Equations With Adaptive Differential Evolution
IEEE Access, 2020 Solving ordinary differential equations (ODEs) is vital in diverse fields. However, it is difficult to obtain the exact analytical solutions of ODEs due to their changeable mathematical forms.
Zijia Zhang, Yaoming Cai, Dongfang Zhang
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A Universal Ordinary Differential Equation
Logical Methods in Computer Science, 2020 An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive continuous function $\epsilon(t)$, it has a $\mathcal{C}^\infty$ solution with $| y(t) - \varphi(t) | & ...
Bournez, Olivier, Pouly, Amaury
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Meromorphic solutions of nonlinear ordinary differential equations [PDF]
, 2010 Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for
Aslan +52 more
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Decomposition of ordinary differential equations
Bulletin of Mathematical Sciences, 2017 Decompositions of linear ordinary differential equations (ode’s) into components of lower order have successfully been employed for determining their solutions. Here this approach is generalized to nonlinear ode’s. It is not based on the existence of Lie
Fritz Schwarz
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