SIAM Journal on Scientific Computing

Article	Citations
Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks	589
Physics-Informed Neural Networks with Hard Constraints for Inverse Design	288
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?	62
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks	58
The Random Feature Model for Input-Output Maps between Banach Spaces	51
Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations	51
An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen--Cahn Equation	51
MIONet: Learning Multiple-Input Operators via Tensor Product	48
Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle	46
Sparse Cholesky Factorization by Kullback--Leibler Minimization	46
Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations	44
On a Novel Fully Decoupled, Second-Order Accurate Energy Stable Numerical Scheme for a Binary Fluid-Surfactant Phase-Field Model	42
Deep Splitting Method for Parabolic PDEs	40
An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems	34
A Stabilizer-Free, Pressure-Robust, and Superconvergence Weak Galerkin Finite Element Method for the Stokes Equations on Polytopal Mesh	33
Improving “Fast Iterative Shrinkage-Thresholding Algorithm”: Faster, Smarter, and Greedier	30
Data-Driven Learning of Nonautonomous Systems	30
Failure-Informed Adaptive Sampling for PINNs	30
The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs	29
Stochastic Rounding and Its Probabilistic Backward Error Analysis	28
A Random Batch Ewald Method for Particle Systems with Coulomb Interactions	25
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates	24
A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties	23
Structure-Preserving, Energy Stable Numerical Schemes for a Liquid Thin Film Coarsening Model	22
Reduced Operator Inference for Nonlinear Partial Differential Equations	22

On Thermodynamically Compatible Finite Volume Schemes for Continuum Mechanics	22
Randomized Quaternion Singular Value Decomposition for Low-Rank Matrix Approximation	22
Overlapping Multipatch Isogeometric Method with Minimal Stabilization	22
Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model	21
Stabilized Scalar Auxiliary Variable Ensemble Algorithms for Parameterized Flow Problems	21
An Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Systems	21
On Greedy Randomized Augmented Kaczmarz Method for Solving Large Sparse Inconsistent Linear Systems	21
An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime	20
Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller--Segel and Poisson--Nernst--Planck Equations	20
Unstructured Space-Time Finite Element Methods for Optimal Control of Parabolic Equations	19
Interpolation-Based Model Order Reduction for Polynomial Systems	18
Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks	18
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control	17
Orthogonal Nonnegative Tucker Decomposition	17
Algorithms for the Rational Approximation of Matrix-Valued Functions	17
Fast Variable Density 3-D Node Generation	16
A Continuous Perspective on Shape Optimization via Domain Transformations	16
Finite Element Discretization Methods for Velocity-Pressure and Stream Function Formulations of Surface Stokes Equations	16
Anderson Acceleration for a Class of Nonsmooth Fixed-Point Problems	16
High Order Semi-implicit WENO Schemes for All-Mach Full Euler System of Gas Dynamics	16
The Aggregated Unfitted Finite Element Method on Parallel Tree-Based Adaptive Meshes	16
Randomized Gram--Schmidt Process with Application to GMRES	16
Data-Driven Balancing of Linear Dynamical Systems	16
Highly Efficient and Energy Dissipative Schemes for the Time Fractional Allen--Cahn Equation	15
An All-at-Once Preconditioner for Evolutionary Partial Differential Equations	15
Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure	15
Implicit Surface Reconstruction With a Curl-Free Radial Basis Function Partition of Unity Method	15
A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs	15
Construct Deep Neural Networks based on Direct Sampling Methods for Solving Electrical Impedance Tomography	15
A Supervised Learning Approach Involving Active Subspaces for an Efficient Genetic Algorithm in High-Dimensional Optimization Problems	15
Parallel Algorithms for Tensor Train Arithmetic	15
Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems	15
Minimization of $L_1$ Over $L_2$ for Sparse Signal Recovery with Convergence Guarantee	14
Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates	14
Algebraic Error Analysis for Mixed-Precision Multigrid Solvers	14
Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness	14
Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights	14
Computing Multiple Solutions of Topology Optimization Problems	14
A Deep Learning Approach for the Computation of Curvature in the Level-Set Method	14
Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems	14
Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose--Einstein Condensates	13
Quality-Bayesian Approach to Inverse Acoustic Source Problems with Partial Data	13
Variable Projection for NonSmooth Problems	13
Minimum Principle on Specific Entropy and High-Order Accurate Invariant-Region-Preserving Numerical Methods for Relativistic Hydrodynamics	13
A Variable Stepsize, Variable Order Family of Low Complexity	13
Evolution of Nonlinear Reduced-Order Solutions for PDEs with Conserved Quantities	13
Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy	13
Fast Iterative Solution of the Optimal Transport Problem on Graphs	13
PIFE-PIC: Parallel Immersed Finite Element Particle-in-Cell for 3-D Kinetic Simulations of Plasma-Material Interactions	13
Nonlinear Preconditioning Strategies for Two-Phase Flows in Porous Media Discretized by a Fully Implicit Discontinuous Galerkin Method	12

Approximation Error Analysis of Some Deep Backward Schemes for Nonlinear PDEs	12
Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization	12
Genetic Column Generation: Fast Computation of High-Dimensional Multimarginal Optimal Transport Problems	12
Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems	12
Two-Phase Segmentation for Intensity Inhomogeneous Images by the Allen--Cahn Local Binary Fitting Model	12
Fast Variable Density Node Generation on Parametric Surfaces with Application to Mesh-Free Methods	12
An Augmented Lagrangian Preconditioner for the Magnetohydrodynamics Equations at High Reynolds and Coupling Numbers	12
Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains	11
Iteratively Reweighted FGMRES and FLSQR for Sparse Reconstruction	11
Functional Tucker Approximation Using Chebyshev Interpolation	11
Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms	11
AMG Preconditioners for Linear Solvers towards Extreme Scale	11
Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models	11
Concurrent MultiParameter Learning Demonstrated on the Kuramoto--Sivashinsky Equation	11
A Multilevel Schwarz Preconditioner Based on a Hierarchy of Robust Coarse Spaces	11
FLUPS: A Fourier-Based Library of Unbounded Poisson Solvers	11
On the Asymptotic Linear Convergence Speed of Anderson Acceleration, Nesterov Acceleration, and Nonlinear GMRES	11
A New Block Preconditioner for Implicit Runge--Kutta Methods for Parabolic PDE Problems	11
Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations	11
A New Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs	10
A Conservative Fully Discrete Numerical Method for the Regularized Shallow Water Wave Equations	10
Two-Dimensional Fourier Continuation and Applications	10
Virtual Elements for the Transmission Eigenvalue Problem on Polytopal Meshes	10
Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems	10
Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis	10
A High-Order Discontinuous Galerkin Method for the Poro-elasto-acoustic Problem on Polygonal and Polyhedral Grids	10
Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting	10
Efficient and Convergent Preconditioned ADMM for the Potts Models	10
Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data	10
Approximating Optimal feedback Controllers of Finite Horizon Control Problems Using Hierarchical Tensor Formats	10
Monolithic Multigrid Methods for Magnetohydrodynamics	10
Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables	10
Explicit Stabilized Integrators for Stiff Optimal Control Problems	9
Fourier-Cosine Method for Finite-Time Gerber--Shiu Functions	9
Asymptotic Preserving IMEX-DG-S Schemes for Linear Kinetic Transport Equations Based on Schur Complement	9
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations	9
Fully Parallel Mesh I/O Using PETSc DMPlex with an Application to Waveform Modeling	9
An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging	9
A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation	9
Stein Variational Reduced Basis Bayesian Inversion	9
Low-Order Preconditioning for the High-Order Finite Element de Rham Complex	9
Variational Bayes' Method for Functions with Applications to Some Inverse Problems	9
A Two-Dimensional Stabilized Discontinuous Galerkin Method on Curvilinear Embedded Boundary Grids	9
Energy Stable and Mass Conservative Numerical Method for Gas Flow in Porous Media with Rock Compressibility	9
Learning Optimal Multigrid Smoothers via Neural Networks	9
A Partition of Unity Method for Divergence-Free or Curl-Free Radial Basis Function Approximation	9
Accurate Front Capturing Asymptotic Preserving Scheme for Nonlinear Gray Radiative Transfer Equation	9
Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks	9
A Conservative Semi-Lagrangian Hybrid Hermite WENO Scheme for Linear Transport Equations and the Nonlinear Vlasov--Poisson System	9
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder	9
PETSc TSAdjoint: A Discrete Adjoint ODE Solver for First-Order and Second-Order Sensitivity Analysis	8
A Generalized Spatially Adaptive Sparse Grid Combination Technique with Dimension-wise Refinement	8
Residual and Restarting in Krylov Subspace Evaluation of the $\varphi$ Function	8
A Well Balanced Finite Volume Scheme for General Relativity	8
Lightning Stokes Solver	8
Randomized Algorithms for Rounding in the Tensor-Train Format	8
Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form	8
Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces	8
Butterfly Factorization Via Randomized Matrix-Vector Multiplications	8
Frequency-Stable Full Maxwell in Electro-quasistatic Gauge	8
Optimization-Based Modal Decomposition for Systems with Multiple Transports	8
On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems	8
Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity	8
Localized Model Reduction for Nonlinear Elliptic Partial Differential Equations: Localized Training, Partition of Unity, and Adaptive Enrichment	8
SuperDC: Superfast Divide-And-Conquer Eigenvalue Decomposition With Improved Stability for Rank-Structured Matrices	8
Lasso Hyperinterpolation Over General Regions	8
Data-Driven Algorithms for Signal Processing with Trigonometric Rational Functions	8
Kaczmarz-Type Inner-Iteration Preconditioned Flexible GMRES Methods for Consistent Linear Systems	8
Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge--Kutta Schemes	8
An Efficient MultiModes Monte Carlo Homogenization Method for Random Materials	8
An H-Multigrid Method for Hybrid High-Order Discretizations	8
Textbook Efficiency: Massively Parallel Matrix-Free Multigrid for the Stokes System	7
High Order Cut Discontinuous Galerkin Methods for Hyperbolic Conservation Laws in One Space Dimension	7
An Efficient Spectral Method for Elliptic PDEs in Complex Domains with Circular Embedding	7
A Parallel-in-Time Algorithm for High-Order BDF Methods for Diffusion and Subdiffusion Equations	7
Sequential Active Learning of Low-Dimensional Model Representations for Reliability Analysis	7
Polynomial Preconditioned Arnoldi with Stability Control	7
High Order Compact Schemes for Flux Type BCs	7
Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances	7
Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments	7

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs	7
A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature	7
Adaptive Finite-Difference Interval Estimation for Noisy Derivative-Free Optimization	7
An Energy Stable $C^0$ Finite Element Scheme for A Phase-Field Model of Vesicle Motion and Deformation	7
A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems	7
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension	7
Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance	7
Parallel Newton--Krylov BDDC and FETI-DP Deluxe Solvers for Implicit Time discretizations of the Cardiac Bidomain Equations	7
A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations	7
Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis	7
Convergence Analysis of BDDC Preconditioners for Composite DG Discretizations of the Cardiac Cell-By-Cell Model	7
Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions	7
$l_p$ Regularization for Ensemble Kalman Inversion	7
Chronos: A General Purpose Classical AMG Solver for High Performance Computing	7
A Three-Operator Splitting Algorithm for Nonconvex Sparsity Regularization	7
Overlapping Domain Decomposition Methods for Ptychographic Imaging	7
Qualitative Indicator Functions for Imaging Crack Networks Using Acoustic Waves	7
MURPHY---A Scalable Multiresolution Framework for Scientific Computing on 3D Block-Structured Collocated Grids	7
Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance	7
Space-Time Block Preconditioning for Incompressible Flow	7
Linearly Implicit Invariant-Preserving Decoupled Difference Scheme For The Rotation-Two-Component Camassa--Holm System	7
Discretization-Error-Accurate Mixed-Precision Multigrid Solvers	7
On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks	6
Discontinuous Galerkin Approximation of the Fully Coupled Thermo-poroelastic Problem	6
SOBMOR: Structured Optimization-Based Model Order Reduction	6
Elastic Wave Propagation in Curvilinear Coordinates with Mesh Refinement Interfaces by a Fourth Order Finite Difference Method	6
A Divergence-Free Stabilized Finite Element Method for the Evolutionary Navier--Stokes Equations	6
The AAAtrig Algorithm for Rational Approximation of Periodic Functions	6
AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)	6
A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations	6
A Globally Convergent Modified Newton Method for the Direct Minimization of the Ohta--Kawasaki Energy with Application to the Directed Self-Assembly of Diblock Copolymers	6
Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation	6
Efficient Numerical Algorithms for the Generalized Langevin Equation	6
Uniform Auxiliary Space Preconditioning for HDG Methods for Elliptic Operators with a Parameter Dependent Low Order Term	6
Mixed Methods for the Velocity-Pressure-Pseudostress Formulation of the Stokes Eigenvalue Problem	6
Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems	6
A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications	6
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning	6
Implicit-Explicit Multirate Infinitesimal GARK Methods	6
State Estimation with Model Reduction and Shape Variability. Application to biomedical problems	6
Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling	6
A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations	6
Efficient Importance Sampling in Quasi-Monte Carlo Methods for Computational Finance	6
Comparison of Accuracy and Scalability of Gauss--Newton and Alternating Least Squares for CANDECOMC/PARAFAC Decomposition	6
A Posteriori Estimator for the Adaptive Solution of a Quasi-Static Fracture Phase-Field Model with Irreversibility Constraints	6
Edge-Promoting Adaptive Bayesian Experimental Design for X-ray Imaging	6
A Conservative Finite Element ALE Scheme for Mass-Conservative Reaction-Diffusion Equations on Evolving Two-Dimensional Domains	6
A Unified Analysis Framework for Iterative Parallel-in-Time Algorithms	6
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation	6
Physics Information Aided Kriging using Stochastic Simulation Models	6
A Direct Eulerian GRP Scheme for a Blood Flow Model in Arteries	6
Computing Edge States without Hard Truncation	6
Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation	6
Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques	6
Control of Bifurcation Structures using Shape Optimization	6
Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations	6
Adaptive Hierarchical Subtensor Partitioning for Tensor Compression	6
A Bound-Preserving and Positivity-Preserving Path-Conservative Discontinuous Galerkin Method for Solving Five-Equation Model of Compressible Two-Medium Flows	6
Discontinuous Galerkin Galerkin Differences for the Wave Equation in Second-Order Form	6
Nonintrusive Reduced-Order Models for Parametric Partial Differential Equations via Data-Driven Operator Inference	5
An Energy-Based, Always Index $\leq$ 1 and Structurally Amenable Electrical Circuit Model	5
Preconditioning Parametrized Linear Systems	5
An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design	5
Generating Extreme-Scale Matrices With Specified Singular Values or Condition Number	5
Deep Neural Networks for Solving Large Linear Systems Arising from High-Dimensional Problems	5
Optimizing Oblique Projections for Nonlinear Systems using Trajectories	5
Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem	5
High-Order Well-Balanced Finite-Volume Schemes for Hydrodynamic Equations With Nonlocal Free Energy	5
Long-Term Analysis of Stochastic Hamiltonian Systems Under Time Discretizations	5
A Three-field Based Optimization Formulation for Flow Simulations in Networks of Fractures on Nonconforming Meshes	5
A Controllability Method for Maxwell's Equations	5
Gaussian Process Subspace Prediction for Model Reduction	5
A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods	5
A Direction Preserving Discretization for Computing Phase-Space Densities	5
Two-Level Nyström--Schur Preconditioner for Sparse Symmetric Positive Definite Matrices	5
Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs	5
A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms	5
Parallel Algorithms for Computing the Tensor-Train Decomposition	5
Error Estimates for a POD Method for Solving Viscous G-Equations in Incompressible Cellular Flows	5
Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition	5
Fast Randomized Non-Hermitian Eigensolvers Based on Rational Filtering and Matrix Partitioning	5
AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models	5
Horseshoe Priors for Edge-Preserving Linear Bayesian Inversion	5
Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems	5
Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models	5
PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology	5
Numerical Simulations of Surface Quasi-Geostrophic Flows on Periodic Domains	5
Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks	5
Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems	5
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators	5
Surface Finite Element Approximation of Spherical Whittle--Matérn Gaussian Random Fields	5
Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo	5
Regularization of Poisson--Boltzmann Type Equations with Singular Source Terms Using the Range-Separated Tensor Format	5
A Scalable and Robust Vertex-Star Relaxation for High-Order FEM	5
Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods	5