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Weighted radial basis collocation method for boundary value problems: WEIGHTED RADIAL BASIS COLLOCATION METHOD
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journal
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September 2006 |
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Least‐squares collocation meshless method
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journal
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July 2001 |
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Fast Parallel Algorithms for Short-Range Molecular Dynamics
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journal
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March 1995 |
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BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one
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journal
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September 1986 |
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Least squares collocation and regularization
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journal
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December 1979 |
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L 1-minimization methods for Hamilton–Jacobi equations: the one-dimensional case
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journal
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February 2008 |
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A least-squares preconditioner for radial basis functions collocation methods
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journal
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July 2005 |
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The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems
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journal
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February 2018 |
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A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
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journal
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April 1978 |
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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
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journal
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April 2020 |
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Physics-informed neural networks for high-speed flows
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March 2020 |
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
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journal
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June 2020 |
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A physics-informed operator regression framework for extracting data-driven continuum models
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journal
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January 2021 |
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Fundamental issues in the representation and propagation of uncertain equation of state information in shock hydrodynamics
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journal
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August 2013 |
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A space–time smooth artificial viscosity method for nonlinear conservation laws
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journal
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February 2013 |
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High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
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journal
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July 2016 |
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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journal
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February 2019 |
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A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 1: The 1-D case
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journal
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June 2019 |
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
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journal
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November 2019 |
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A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
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January 2020 |
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Constraint-aware neural networks for Riemann problems
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May 2020 |
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Error bounds for approximations with deep ReLU networks
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journal
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October 2017 |
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Least-squares collocation
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journal
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January 1978 |
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Atomistic shock Hugoniot simulation of single-crystal copper
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journal
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October 2004 |
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Polymorphic transitions in single crystals: A new molecular dynamics method
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December 1981 |
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Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability
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August 2015 |
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Direct simulation Monte Carlo on petaflop supercomputers and beyond
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journal
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August 2019 |
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Solving high-dimensional partial differential equations using deep learning
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August 2018 |
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A Liouville-operator derived measure-preserving integrator for molecular dynamics simulations in the isothermal–isobaric ensemble
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journal
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April 2006 |
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Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool
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December 2009 |
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Centred TVD schemes for hyperbolic conservation laws
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January 2000 |
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Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
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November 2018 |
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Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations
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May 2001 |
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Multiscale modeling of shock wave localization in porous energetic material
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journal
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January 2018 |
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Direct simulation Monte Carlo investigation of the Rayleigh-Taylor instability
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August 2016 |
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Gas-kinetic simulation of sustained turbulence in minimal Couette flow
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July 2018 |
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The Riemann problem for fluid flow of real materials
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January 1989 |
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Artificial neural networks for solving ordinary and partial differential equations
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January 1998 |
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Taking on the curse of dimensionality in joint distributions using neural networks
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May 2000 |
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Viscous Regularization of the Euler Equations and Entropy Principles
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journal
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January 2014 |
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Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
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journal
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January 2020 |
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Convex Entropies and Hyperbolicity for General Euler Equations
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journal
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December 1998 |
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Limitations of Physics Informed Machine Learning for Nonlinear Two-Phase Transport in Porous Media
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journal
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January 2020 |
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Vanishing viscosity solutions of nonlinear hyperbolic systems
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journal
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January 2005 |
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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
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journal
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June 2020 |
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A fast algorithm for solving first-order PDEs by L1-minimization
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journal
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January 2008 |