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 2020-05-01 to 2024-05-01.)

Article	Citations
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations	264
Dying ReLU and Initialization: Theory and Numerical Examples	111
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs	105
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks	85
Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method	72
A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem	52
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks	51
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains	51
Deep Network Approximation Characterized by Number of Neurons	40
A Third Order BDF Energy Stable Linear Scheme for the No-Slope-Selection Thin Film Model	38
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	32
Finite Neuron Method and Convergence Analysis	31
Machine Learning and Computational Mathematics	24
DAFI: An Open-Source Framework for Ensemble-Based Data Assimilation and Field Inversion	22
A Novel Full-Euler Low Mach Number IMEX Splitting	22
An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems	22
Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units	21
Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains	21
Target-Oriented Inversion of Time-Lapse Seismic Waveform Data	20
DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data	17
A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows	17
Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems	16
A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales	16
The Riemann Problem for a Blood Flow Model in Arteries	16

A Study of Several Artiﬁcial Viscosity Models within the Discontinuous Galerkin Framework	15
A Wavelet-Adaptive Method for Multiscale Simulation of Turbulent Flows in Flying Insects	14
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations	14
Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations	14
High Order Conservative Semi-Lagrangian Scheme for the BGK Model of the Boltzmann Equation	13
Multiple-Scattering $T$-Matrix Simulations for Nanophotonics: Symmetries and Periodic Lattices	13
A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation	13
Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations	12
Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model	12
A Compressible Conserved Discrete Unified Gas-Kinetic Scheme with Unstructured Discrete Velocity Space for Multi-Scale Jet Flow Expanding into Vacuum Environment	12
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning	12
Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws	12
Modelling Thermo-Electro-Mechanical Effects in Orthotropic Cardiac Tissue	12
On a Hybrid Approach for Recovering Multiple Obstacles	11
A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space	11
Active Nematodynamics on Curved Surfaces – The Influence of Geometric Forces on Motion Patterns of Topological Defects	11
Convergence Rate Analysis for Deep Ritz Method	10
NeuronSeg_BACH: Automated Neuron Segmentation Using B-Spline Based Active Contour and Hyperelastic Regularization	10
Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations	10
Physics-Driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks	10
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study	10
Ensemble Gradient for Learning Turbulence Models from Indirect Observations	9
A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem	9
On False Accuracy Verification of UMUSCL Scheme	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
An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation	9
Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models	9
A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model	9
A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method	9
A Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear Grids	9
Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model	8
Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term	8
Phase-Field-Based Axisymmetric Lattice Boltzmann Method for Two-Phase Electro-Hydrodynamic Flows	8
An All Speed Second Order IMEX Relaxation Scheme for the Euler Equations	8
A Deep Spatio-Temporal Forecasting Model for Multi-Site Weather Prediction Post-Processing	8
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression	7
A Hodge Decomposition Method for Dynamic Ginzburg–Landau Equations in Nonsmooth Domains — A Second Approach	7
A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations	7
High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres	7
Direct Simulation of Charge Transport in Graphene Nanoribbons	7
AWeighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling	7
One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes	7
Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability	7
$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem	7
Towards a Theoretical Background for Strong-Scattering Inversion – Direct Envelope Inversion and Gel’fand-Levitan-Marchenko Theory	7
Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method	7
A Hybrid Immersed Boundary-Lattice Boltzmann Method for Simulation of Viscoelastic Fluid Flows Interaction with Complex Boundaries	7
Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem	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
How does Gauge Cooling Stabilize Complex Langevin?	6
Enforcing Imprecise Constraints on Generative Adversarial Networks for Emulating Physical Systems	6
Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations	6
A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs	6
High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes	6
Performance Enhancement for High-Order Gas-Kinetic Scheme Based on WENO-Adaptive-Order Reconstruction	6
EMPIRE-PIC: A Performance Portable Unstructured Particle-in-Cell Code	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
An Adaptive Modal Discontinuous Galerkin Finite Element Parallel Method Using Unsplit Multi-Axial Perfectly Matched Layer for Seismic Wave Modeling	5
Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion	5
Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow	5
Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning	5
Modified Ghost Fluid Method with Axisymmetric Source Correction (MGFM/ASC)	5
Deep Unfitted Nitsche Method for Elliptic Interface Problems	5
Constraint Energy Minimizing Generalized MultiscaleFiniteElementMethodforHigh-Contrast Linear Elasticity Problem	5
An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence	5
Shallow Water Moment Models for Bedload Transport Problems	5
A Modified Adaptive Improved Mapped WENO Method	5
Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System	5
Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media	5
Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes	5
Elastic Characteristics of Digital Cores from Longmaxi Shale Using Lattice Spring Models	5
Heterogeneity Spectrum of Earth’s Upper Mantle Obtained from the Coherence of Teleseismic PWaves	5
Unconditional Positivity-Preserving and Energy StableSchemesforaReducedPoisson-Nernst-Planck System	5
An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions	5
Bayesian Model Calibration with Interpolating Polynomials based on Adaptively Weighted Leja Nodes	5
A Decreasing Upper Bound of the Energy for Time-Fractional Phase-Field Equations	5
Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model	5
An Improved Gas-Kinetic Scheme for Multimaterial Flows	5
Random Batch Particle Methods for the Homogeneous Landau Equation	4
Structure-Preserving Numerical Methods for Stochastic Poisson Systems	4
A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation	4
Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation	4
Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap	4
Stochastic Multiscale Heat Transfer Analysis of Heterogeneous Materials with Multiple Random Configurations	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
Tuning Symplectic Integrators is Easy and Worthwhile	4
Saturation-Value Blind Color Image Deblurring with Geometric Spatial-Feature Prior	4
High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes	4
A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection	4
A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations	4
Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh	4
A New Mapped WENO Scheme Using Order-Preserving Mapping	4
Hybrid Diffuse and Sharp Interface Immersed Boundary Methods for Particulate Flows in the Presence of Complex Boundaries	4
Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study	4
A Colocalized Scheme for Three-Temperature Grey Diffusion Radiation Hydrodynamics	4
A General Algorithm for Calculating Irreducible Brillouin Zones	4
Fast One-Dimensional Convolution with General Kernels Using Sum-of-Exponential Approximation	4