Results 71 to 80 of about 37,100 (232)
Solving inverse source problems for linear PDEs using sparse sensor measurements
2016 50th Asilomar Conference on Signals, Systems and Computers, 2016 Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some intelligent data analysis tools on the samples.
Murray-Bruce, J, Dragotti, PL
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International Journal for Numerical Methods in Fluids, EarlyView.This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime +3 more
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Heat Transfer, EarlyView.ABSTRACT Traditional numerical methods, such as finite difference methods (FDM), finite element methods (FEM), and spectral methods, often face meshing challenges and high computational cost for solving nonlinear coupled differential equations. Machine learning techniques, specifically Physics‐informed machine learning, address these obstacles by ...
Ahmad, Feroz Soomro, Husna Zafar
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Partial Differential Equations in Applied MathematicsThis article employs the Laplace transform approach to solve the Bagley–Torvik equation including Caputo’s fractional derivative. Laplace transform is a powerful method for enabling solving integer and non-integer order ODEs and PDEs in engineering and ...
Dania Santina +4 more
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A General Method for the Solution of Inverse Problems in Transport Phenomena
Chemical Engineering Transactions, 2015 The typical inverse problems in transport phenomena are given by partial differential equations with unknown boundary conditions, which are to be estimated from measurements corresponding to solutions of the PDEs or of their gradients.
M. Vocciante, A. Reverberi, V. Dovi
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Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients [PDF]
, 2022 Venkateswaran P. Krishnan +2 more
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On inverse problems for several coupled PDE systems arising in mathematical biology
Journal of Mathematical Biology, 2023 In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic ...
Ming-Hui Ding +2 more
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Limnology and Oceanography: Methods, EarlyView.Abstract Estimating exchange rates of submarine groundwater discharge (SGD) at high temporal resolution over extended periods remains challenging, particularly when using heat as a tracer in highly dynamic environments such as tidal systems. Currently available heat transport models struggle to accurately quantify SGD exchange rates in these settings ...
S. Frei +3 more
wiley +1 more source
Mathematical Modelling and AnalysisIn this paper, we mainly study the numerical differentiation problem of computing the fractional order derivatives from noise data of a single variable function.
Zewen Wang +3 more
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CUQIpy: II. Computational uncertainty quantification for PDE-based inverse problems in Python [PDF]
Inverse ProblemsAbstract Inverse problems, particularly those governed by Partial Differential Equations (PDEs), are prevalent in various scientific and engineering applications, and uncertainty quantification (UQ) of solutions to these problems is essential for informed decision-making.
Amal Alghamdi +6 more
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