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An enhanced V-cycle MgNet model for operator learning in numerical partial differential equations
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial...
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Differential Equations
Differential equations govern numerous problems in physics, engineering, biology, and earth sciences. Chapter 8 starts providing the basics to work...
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Basic Equations of Atmospheric Turbulence
Before starting the derivation of the equations for the turbulent fluxes of momentum, heat and trace gases (Sect. 2.3), we present a short...
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Constitutive Equations
Hooke’s law which relates the stress tensor to the strain tensor in linear elastic materials, was introduced in Chap. 3...
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Comparative Analysis and Unified Derivation of Reissner’s Equations for 2D Bending of Thick Plates and Timoshenko’s Equations for Bending of Beams
AbstractCurrently, bending deformations of lithospheric plates are calculated based on Kirchhoff’s theory of bending of thin plates, which was...
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Nonlinear Geodetic Equations with Uncertainties: Algebraic-Numeric Solutions
Techniques for solution of nonlinear equations where coefficients or parameters are uncertain are considered. An algebraic based nonlinear...
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Inverse Flood Routing Using Simplified Flow Equations
The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of...
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The waveform comparison of three fractional viscous acoustic wave equations
The forward simulation of the viscous acoustic wave equation is essential for understanding wave propagation and seismic inversion. The viscous...
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Modelling disease spread with spatio-temporal fractional derivative equations and saturated incidence rate
The global analysis of a spatio-temporal fractional order SIR infection model with saturated incidence function is suggested and studied in this...
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Data-driven discovery of governing equations for transient heat transfer analysis
With the development of automatic measurement and data storage, vast quantities of data can be recorded and analyzed for heat transfer processes,...
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On the initialization of the sensitivity matrix in variational equations
We address a claim frequently raised by one author that determination of Earth’s gravity field by satellite observations using traditional methods is...
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Deep learning discovery of macroscopic governing equations for viscous gravity currents from microscopic simulation data
Although deep learning has been successfully applied in a variety of science and engineering problems owing to its strong high-dimensional nonlinear...
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Integrated wellbore-reservoir modeling based on 3D Navier–Stokes equations with a coupled CFD solver
The occurrence of fluid flow near a wellhead is the major concern of the petroleum industry, as pressure drop, loss of formation, and other variables...
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Numerical modeling based on the improved BSO algorithm for asymmetric elastic wave equations
With the continuous research in seismology, the influence of the heterogeneity caused by microstructure interactions of the medium on seismic wave...