6 citations · 21 across the 21 of their papers we have counts for
22 papers
Graph Neural Multilevel Preconditioners for Iterative Solvers
Zechen Zhang, Rui Peng Li, Yousef Saad
Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning. While classica…
Factored Sparse Approximate Inverse Preconditioning via Spectral Optimization
Francesco Brarda, Tianshi Xu, Vassilis Kalantzis +2
In this paper, we study value selection for fixed-pattern factorized sparse approximate inverse preconditioners. Given a prescribed sparsity pattern for a factor we choose its…
Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
Ming Kang, Hang Li, Qiwen Tan +5
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equa…
LE-PDE++: Mamba for accelerating PDEs Simulations
Aoming Liang, Zhaoyang Mu, Qi liu +3
Partial Differential Equations are foundational in modeling science and natural systems such as fluid dynamics and weather forecasting. The Latent Evolution of PDEs method is desig…
Multiscale Neural Networks for Approximating Green's Functions
Wenrui Hao, Rui Peng Li, Yuanzhe Xi +2
Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solv…
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
Shuhao Cao, Francesco Brarda, Ruipeng Li +1
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, t…
Reducing operator complexity in Algebraic Multigrid with Machine Learning Approaches
Ru Huang, Kai Chang, Huan He +2
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of…
Optimizing Irregular Communication with Neighborhood Collectives and Locality-Aware Parallelism
Gerald Collom, Rui Peng Li, Amanda Bienz
Irregular communication often limits both the performance and scalability of parallel applications. Typically, applications individually implement irregular messages using point-to…
A Two-level GPU-Accelerated Incomplete LU Preconditioner for General Sparse Linear Systems
Tianshi Xu, Ruipeng Li, Daniel Osei-Kuffuor
This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems.…
Multilevel-in-Layer Training for Deep Neural Network Regression
Colin Ponce, Ruipeng Li, Christina Mao +1
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of st…
parGeMSLR: A Parallel Multilevel Schur Complement Low-Rank Preconditioning and Solution Package for General Sparse Matrices
Tianshi Xu, Vassilis Kalantzis, Ruipeng Li +3
This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distribute…
Neumann Series in GMRES and Algebraic Multigrid Smoothers
Stephen Thomas, Arielle Carr, Paul Mullowney +2
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to…
Learning optimal multigrid smoothers via neural networks
Ru Huang, Ruipeng Li, Yuanzhe Xi
Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning…
The computation of seismic normal modes with rotation as a quadratic eigenvalue problem
Jia Shi, Ruipeng Li, Yuanzhe Xi +2
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the prese…
Parallel Approximate Ideal Restriction Multigrid for Solving the S Transport Equations
Joshua Hanophy, Ben S. Southworth, Ruipeng Li +2
The computational kernel in solving the transport equations is the parallel sweep, which corresponds to directly inverting a block lower triangular linear system that arises…
A non-perturbative approach to computing seismic normal modes in rotating planets
Jia Shi, Ruipeng Li, Yuanzhe Xi +2
A Continuous Galerkin method-based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in th…
The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
Ruipeng Li, Yuanzhe Xi, Lucas Erlandson +1
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its n…
On Parallel Solution of Sparse Triangular Linear Systems in CUDA
Ruipeng Li
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Signific…
Fast computation of spectral densities for generalized eigenvalue problems
Yuanzhe Xi, Ruipeng Li, Yousef Saad
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in ph…
A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski +2
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywh…
Low-rank correction methods for algebraic domain decomposition preconditioners
Ruipeng Li, Yousef Saad
This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework…
Schur Complement based domain decomposition preconditioners with Low-rank corrections
Ruipeng Li, Yuanzhe Xi, Yousef Saad
This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD)…