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Advances in continuous and discrete models最新文献

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Computing confined elasticae 计算受限弹性
Pub Date : 2022-03-17 DOI: 10.1186/s13662-022-03731-7
S. Bartels, Pascal Weyer
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引用次数: 1
Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations 演化Navier-Stokes方程二阶时间数值离散化的收敛性
Pub Date : 2022-03-01 DOI: 10.1186/s13662-022-03736-2
L. Berselli, S. Spirito
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引用次数: 0
Partial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switching 具有马尔可夫切换的中性受电弓随机微分方程的部分渐近稳定性
Pub Date : 2022-02-25 DOI: 10.1186/s13662-022-03692-x
Lassaad Mchiri, T. Caraballo, Mohamed Rhaima
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引用次数: 2
Geometric properties of the meromorphic functions class through special functions associated with a linear operator 通过与线性算子相关的特殊函数研究亚纯函数类的几何性质
Pub Date : 2022-02-19 DOI: 10.1186/s13662-022-03691-y
F. Ghanim, H. Al‐Janaby, O. Bazighifan
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引用次数: 5
The Lax pair structure for the spin Benjamin–Ono equation 自旋Benjamin-Ono方程的Lax对结构
Pub Date : 2022-02-16 DOI: 10.1186/s13662-023-03768-2
P. G'erard
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引用次数: 5
Analytical analysis of fractional-order sequential hybrid system with numerical application 分数阶序列混合系统的解析分析及其数值应用
Pub Date : 2022-02-02 DOI: 10.1186/s13662-022-03685-w
Aziz Khan, Z. Khan, T. Abdeljawad, H. Khan
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引用次数: 20
Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel 基于勒让德多项式的神经网络在多孔通道中非牛顿流体传热传质分析中的应用
Pub Date : 2022-01-22 DOI: 10.1186/s13662-022-03676-x
N. A. Khan, M. Sulaiman, P. Kumam, F. Alarfaj
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引用次数: 7
Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations 随机系数随机最优控制及相关随机Hamilton-Jacobi-Bellman方程
Pub Date : 2022-01-14 DOI: 10.1186/s13662-021-03674-5
Jun Moon
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引用次数: 0
A physics-informed neural network to model COVID-19 infection and hospitalization scenarios. 用于模拟 COVID-19 感染和住院情况的物理信息神经网络。
IF 2.3 Q1 MATHEMATICS Pub Date : 2022-01-01 Epub Date: 2022-10-27 DOI: 10.1186/s13662-022-03733-5
Sarah Berkhahn, Matthias Ehrhardt

In this paper, we replace the standard numerical approach of estimating parameters in a mathematical model using numerical solvers for differential equations with a physics-informed neural network (PINN). This neural network requires a sequence of time instances as direct input of the network and the numbers of susceptibles, vaccinated, infected, hospitalized, and recovered individuals per time instance to learn certain parameters of the underlying model, which are used for the loss calculations. The established model is an extended susceptible-infected-recovered (SIR) model in which the transitions between disease-related population groups, called compartments, and the physical laws of epidemic transmission dynamics are expressed by a system of ordinary differential equations (ODEs). The system of ODEs and its time derivative are included in the residual loss function of the PINN in addition to the data error between the current network output and the time series data of the compartment sizes. Further, we illustrate how this PINN approach can also be used for differential equation-based models such as the proposed extended SIR model, called SVIHR model. In a validation process, we compare the performance of the PINN with results obtained with the numerical technique of non-standard finite differences (NSFD) in generating future COVID-19 scenarios based on the parameters identified by the PINN. The used training data set covers the time between the outbreak of the pandemic in Germany and the last week of the year 2021. We obtain a two-step or hybrid approach, as the PINN is then used to generate a future COVID-19 outbreak scenario describing a possibly next pandemic wave. The week at which the prediction starts is chosen in mid-April 2022.

在本文中,我们用物理信息神经网络(PINN)取代了使用微分方程数值求解器估算数学模型参数的标准数值方法。该神经网络需要一连串的时间实例作为网络的直接输入,以及每个时间实例中易感者、接种疫苗者、感染者、住院者和康复者的人数,从而学习基础模型的某些参数,这些参数用于损失计算。已建立的模型是一个扩展的易感-感染-康复(SIR)模型,其中与疾病相关的人群(称为区隔)之间的转换以及流行病传播动态的物理规律由一个常微分方程(ODE)系统表示。除了当前网络输出与分区大小时间序列数据之间的数据误差外,PINN 的残差损失函数中还包括 ODE 系统及其时间导数。此外,我们还说明了这种 PINN 方法如何也能用于基于微分方程的模型,如拟议的扩展 SIR 模型,即 SVIHR 模型。在验证过程中,我们比较了 PINN 和非标准有限差分数值技术(NSFD)在根据 PINN 确定的参数生成未来 COVID-19 场景方面的性能。所使用的训练数据集涵盖了从德国爆发大流行病到 2021 年最后一周之间的时间。我们采用两步法或混合法,利用 PINN 生成 COVID-19 的未来疫情,描述可能出现的下一波大流行。预测的起始周选在 2022 年 4 月中旬。
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引用次数: 0
Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity. 具有不完全免疫力的 SIVR 流行模型的动力学分析与优化控制
IF 2.3 Q1 MATHEMATICS Pub Date : 2022-01-01 Epub Date: 2022-07-18 DOI: 10.1186/s13662-022-03723-7
Yiming Liu, Shuang Jian, Jianguo Gao

In this paper, we establish an SIVR model with diffusion, spatially heterogeneous, latent infection, and incomplete immunity in the Neumann boundary condition. Firstly, the threshold dynamic behavior of the model is proved by using the operator semigroup method, the well-posedness of the solution and the basic reproduction number 0 are given. When 0 < 1 , the disease-free equilibrium is globally asymptotically stable, the disease will be extinct; when 0 > 1 , the epidemic equilibrium is globally asymptotically stable, the disease will persist with probability one. Then, we introduce the patient's treatment into the system as the control parameter, and the optimal control of the system is discussed by applying the Hamiltonian function and the adjoint equation. Finally, the theoretical results are verified by numerical simulation.

本文在新曼边界条件下建立了一个具有扩散、空间异质性、潜伏感染和不完全免疫的 SIVR 模型。首先,利用算子半群法证明了该模型的阈值动态行为,给出了解的拟合优度和基本繁殖数ℜ 0。当 ℜ 0 1 时,无病均衡是全局渐近稳定的,疾病将灭绝;当 ℜ 0 > 1 时,流行均衡是全局渐近稳定的,疾病将以 1 的概率持续存在。然后,我们将病人的治疗作为控制参数引入系统,并应用哈密顿函数和邻接方程讨论了系统的最优控制。最后,通过数值模拟验证了理论结果。
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引用次数: 0
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Advances in continuous and discrete models
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