Related papers: Mapping Sparse Triangular Solves to GPUs via Fine-…

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…

Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…

We propose the first GPU algorithm for the 3D triangulation refinement problem. For an input of a piecewise linear complex $\mathcal{G}$ and a constant $B$, it produces, by adding Steiner points, a constrained Delaunay triangulation…

We present a novel linear solver that works well for large systems obtained from discretizing PDEs. It is robust and, for the examples we studied, the computational effort scales linearly with the number of equations. The algorithm is based…

We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…

Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses…

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering…

Statistical preconditioning enables fast methods for distributed large-scale empirical risk minimization problems. In this approach, multiple worker nodes compute gradients in parallel, which are then used by the central node to update the…

In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…

Current AI training infrastructure is dominated by single instruction multiple data (SIMD) and systolic array architectures, such as Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs), that excel at accelerating parallel…

We present a fully Julia-based, GPU-accelerated workflow for solving large-scale sparse nonlinear optimal control problems. Continuous-time dynamics are modeled and then discretized via direct transcription with \texttt{OptimalControl.jl}…

The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems…

A major bottleneck in scenario-based Sample Average Approximation (SAA) for stochastic programming (SP) is the cost of solving an exact second-stage problem for every scenario, especially when each scenario contains an NP-hard combinatorial…

As neural network model sizes have dramatically increased, so has the interest in various techniques to reduce their parameter counts and accelerate their execution. An active area of research in this field is sparsity - encouraging zero…