Related papers: MURPHY -- A scalable multiresolution framework for…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
To mitigate communication overheads in distributed model training, several studies propose the use of compressed stochastic gradients, usually achieved by sparsification or quantization. Such techniques achieve high compression ratios, but…
Scaling large language models has driven remarkable advancements across various domains, yet the continual increase in model size presents significant challenges for real-world deployment. The Mixture of Experts (MoE) architecture offers a…
This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid…
This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The circuit ordinary differential equations are first rewritten by a system of…
The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has been reported to be the most efficient algorithm for computing…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Federated learning enables collaborative model training across distributed clients while preserving data privacy. However, in practical deployments, device heterogeneity, non-independent, and identically distributed (Non-IID) data often…
In this paper we show that our Machine Learning (ML) approach, CoMLSim (Composable Machine Learning Simulator), can simulate PDEs on highly-resolved grids with higher accuracy and generalization to out-of-distribution source terms and…
This article presents the development and validation of a hybrid multi-sphere discrete element framework - Rigid3D, for the simulation of granular systems with arbitrarily shaped particles in 3D space. In this DEM framework, a non-spherical…
Data management is becoming increasingly important in dealing with the large amounts of data produced by large-scale scientific simulations and instruments. Existing multilevel compression algorithms offer a promising way to manage…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…
A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…