OOIR: Observatory of International Research

Papers

(The TQCC of Communications in Computational Physics is 4. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-03-01 to 2024-03-01.)

Article	Citations
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations	248
Dying ReLU and Initialization: Theory and Numerical Examples	105
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs	97
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks	76
Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method	70
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks	47
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains	46
A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem	44
A Third Order BDF Energy Stable Linear Scheme for the No-Slope-Selection Thin Film Model	37
Deep Network Approximation Characterized by Number of Neurons	36
A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters	36
Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions	31
Finite Neuron Method and Convergence Analysis	30
A Novel Full-Euler Low Mach Number IMEX Splitting	22
Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units	21
Machine Learning and Computational Mathematics	20
DAFI: An Open-Source Framework for Ensemble-Based Data Assimilation and Field Inversion	19
An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems	19
Target-Oriented Inversion of Time-Lapse Seismic Waveform Data	19
Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains	18
DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data	16
Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems	15
A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales	15
Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations	14
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations	14

The Riemann Problem for a Blood Flow Model in Arteries	14
A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows	13
A Study of Several Artiﬁcial Viscosity Models within the Discontinuous Galerkin Framework	13
High Order Conservative Semi-Lagrangian Scheme for the BGK Model of the Boltzmann Equation	13
A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation	12
Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model	12
A Wavelet-Adaptive Method for Multiscale Simulation of Turbulent Flows in Flying Insects	12
Multiple-Scattering $T$-Matrix Simulations for Nanophotonics: Symmetries and Periodic Lattices	12
Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations	11
A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space	11
Modelling Thermo-Electro-Mechanical Effects in Orthotropic Cardiac Tissue	11
Active Nematodynamics on Curved Surfaces – The Influence of Geometric Forces on Motion Patterns of Topological Defects	11
Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws	11
Convergence Rate Analysis for Deep Ritz Method	10
NeuronSeg_BACH: Automated Neuron Segmentation Using B-Spline Based Active Contour and Hyperelastic Regularization	10
A Compressible Conserved Discrete Unified Gas-Kinetic Scheme with Unstructured Discrete Velocity Space for Multi-Scale Jet Flow Expanding into Vacuum Environment	10
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning	10
Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations	10
A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model	9
An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation	9
Ensemble Gradient for Learning Turbulence Models from Indirect Observations	9
A Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear Grids	9
Improved RBF Collocation Methods for Fourth Order Boundary Value Problems	9
Partitioned and Monolithic Algorithms for the Numerical Solution of Cardiac Fluid-Structure Interaction	9
Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models	9
An All Speed Second Order IMEX Relaxation Scheme for the Euler Equations	8
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study	8
A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing	8
On False Accuracy Verification of UMUSCL Scheme	8
On a Hybrid Approach for Recovering Multiple Obstacles	8
Physics-Driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks	7
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression	7
Towards a Theoretical Background for Strong-Scattering Inversion – Direct Envelope Inversion and Gel’fand-Levitan-Marchenko Theory	7
A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations	7
A Hybrid Immersed Boundary-Lattice Boltzmann Method for Simulation of Viscoelastic Fluid Flows Interaction with Complex Boundaries	7
Direct Simulation of Charge Transport in Graphene Nanoribbons	7
A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem	7
One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes	7
A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method	7
$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem	7
A Hodge Decomposition Method for Dynamic Ginzburg–Landau Equations in Nonsmooth Domains — A Second Approach	7
Phase-Field-Based Axisymmetric Lattice Boltzmann Method for Two-Phase Electro-Hydrodynamic Flows	7
Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term	7
Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability	6
High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres	6
A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs	6
Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method	6
How does Gauge Cooling Stabilize Complex Langevin?	6
Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem	6
Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model	6

Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences	6
Random Batch Algorithms for Quantum Monte Carlo Simulations	6
Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations	6
EMPIRE-PIC: A Performance Portable Unstructured Particle-in-Cell Code	6
Local Discrete Velocity Grids for Multi-Species Rarefied Flow Simulations	6
A Coupled FEM-BEM Approach for the Solution of the Free-Boundary Axi-Symmetric Plasma Equilibrium Problem	6
AWeighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling	6
Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model	5
Bayesian Model Calibration with Interpolating Polynomials based on Adaptively Weighted Leja Nodes	5
An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence	5
Performance Enhancement for High-Order Gas-Kinetic Scheme Based on WENO-Adaptive-Order Reconstruction	5
Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media	5
An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions	5
Elastic Characteristics of Digital Cores from Longmaxi Shale Using Lattice Spring Models	5
High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes	5
An Adaptive Modal Discontinuous Galerkin Finite Element Parallel Method Using Unsplit Multi-Axial Perfectly Matched Layer for Seismic Wave Modeling	5
Unconditional Positivity-Preserving and Energy StableSchemesforaReducedPoisson-Nernst-Planck System	5
Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning	5
Constraint Energy Minimizing Generalized MultiscaleFiniteElementMethodforHigh-Contrast Linear Elasticity Problem	5
An Improved Gas-Kinetic Scheme for Multimaterial Flows	5
Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems	5
Heterogeneity Spectrum of Earth’s Upper Mantle Obtained from the Coherence of Teleseismic PWaves	5
Shallow Water Moment Models for Bedload Transport Problems	5
A Modified Adaptive Improved Mapped WENO Method	5
Tuning Symplectic Integrators is Easy and Worthwhile	4
Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study	4
High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes	4
Deep Unfitted Nitsche Method for Elliptic Interface Problems	4
Fast One-Dimensional Convolution with General Kernels Using Sum-of-Exponential Approximation	4
Random Batch Particle Methods for the Homogeneous Landau Equation	4
Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System	4
Structure-Preserving Numerical Methods for Stochastic Poisson Systems	4
Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation	4
Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow	4
Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes	4
Implementation of Finite Difference Weighted Compact Nonlinear Schemes with the Two-Stage Fourth-Order Accurate Temporal Discretization	4
A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems	4
Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh	4
Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion	4
A Colocalized Scheme for Three-Temperature Grey Diffusion Radiation Hydrodynamics	4
Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap	4
A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations	4
A New Mapped WENO Scheme Using Order-Preserving Mapping	4
Modified Ghost Fluid Method with Axisymmetric Source Correction (MGFM/ASC)	4