A stable Petrov-Galerkin method for convection-dominated problems
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January 1997 |
State of the Art Report on Mathematical Methods for Groundwater Pollution Source Identification
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January 2001 |
A unified deep artificial neural network approach to partial differential equations in complex geometries
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November 2018 |
A high-order discontinuous Galerkin method for unsteady advection–diffusion problems
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March 2017 |
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
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September 1982 |
A Limited Memory Algorithm for Bound Constrained Optimization
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September 1995 |
Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
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March 2021 |
High order finite difference numerical methods for time-dependent convection–dominated problems
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November 2005 |
Approximation by superpositions of a sigmoidal function
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December 1989 |
A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations
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August 2009 |
Physics Informed Extreme Learning Machine (PIELM)–A rapid method for the numerical solution of partial differential equations
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May 2020 |
A summary of numerical methods for time-dependent advection-dominated partial differential equations
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March 2001 |
Bubble functions prompt unusual stabilized finite element methods
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June 1995 |
Stabilized finite element methods: I. Application to the advective-diffusive model
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March 1992 |
An ‘upwind’ finite element scheme for two-dimensional convective transport equation
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January 1977 |
Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport
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July 2020 |
A multidimensional streamline-based method to simulate reactive solute transport in heterogeneous porous media
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July 2010 |
Positive Solution of Two-Dimensional Solute Transport in Heterogeneous Aquifers
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November 2006 |
Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems
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February 2016 |
Multilayer feedforward networks are universal approximators
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January 1989 |
A finite element solution for the fractional advection–dispersion equation
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December 2008 |
A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations
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May 1989 |
A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
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March 1986 |
Conservation properties for the Galerkin and stabilised forms of the advection–diffusion and incompressible Navier–Stokes equations
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March 2005 |
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
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January 2020 |
Neural-network methods for boundary value problems with irregular boundaries
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January 2000 |
Neural algorithm for solving differential equations
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November 1990 |
Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
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November 2007 |
Physics-informed neural networks for high-speed flows
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March 2020 |
One-dimensional linear advection–diffusion equation: Analytical and finite element solutions
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January 2015 |
Adjoint method for obtaining backward-in-time location and travel time probabilities of a conservative groundwater contaminant
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November 1999 |
An upstream finite element method for solution of transient transport equation in fractured porous media
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June 1982 |
A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation
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July 1988 |
fPINNs: Fractional Physics-Informed Neural Networks
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January 2019 |
Contaminant transport through porous media: An overview of experimental and numerical studies
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March 2014 |
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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February 2019 |
High Order Difference Schemes for Unsteady One-Dimensional Diffusion-Convection Problems
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September 1994 |
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
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April 2020 |
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
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June 2020 |
DGM: A deep learning algorithm for solving partial differential equations
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December 2018 |
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
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April 2020 |
Investigating the Effects of Anisotropic Mass Transport on Dendrite Growth in High Energy Density Lithium Batteries
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November 2015 |
Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems
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May 2020 |
Optimal weighting in the finite difference solution of the convection-dispersion equation
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December 1997 |
The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems
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February 2018 |
Modeling fluid flow and transport in variably saturated porous media with the STOMP simulator. 1. Nonvolatile three-phase model description
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January 1995 |
Two numerical methods for solving a backward heat conduction problem
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August 2006 |
Numerical solution of unsteady advection dispersion equation arising in contaminant transport through porous media using neural networks
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August 2016 |
Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks
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January 2021 |