Related papers: A High-Performance Implementation of a Robust Prec…
In this paper we describe how DUNE, an open source scientific software framework, is developed. Having a sustainable software framework for the solution of partial differential equations is the main driver of DUNE's development. We take a…
In this work we focus on the preconditioning of a Galerkin space-time isogeometric discretization of the heat equation. Exploiting the tensor product structure of the basis functions in the parametric domain, we propose a preconditioner…
PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…
Despite the success of Generative Adversarial Networks (GANs), their training suffers from several well-known problems, including mode collapse and difficulties learning a disconnected set of manifolds. In this paper, we break down the…
The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers.…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
Motivated by a wide range of real-world problems whose solutions exhibit boundary and interior layers, the numerical analysis of discretizations of singularly perturbed differential equations is an established sub-discipline within the…
A new domain decomposition preconditioner is introduced for efficiently solving linear systems Ax = b with a symmetric positive definite matrix A. The particularity of the new preconditioner is that it is not necessary to have access to the…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…
In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…
We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to…
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Large-scale GPU traces play a critical role in identifying performance bottlenecks within heterogeneous High-Performance Computing (HPC) architectures. However, the sheer volume and complexity of a single trace of data make performance…
This paper introduces HEPPO-GAE, an FPGA-based accelerator designed to optimize the Generalized Advantage Estimation (GAE) stage in Proximal Policy Optimization (PPO). Unlike previous approaches that focused on trajectory collection and…
Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We have extended the Falkon lightweight task execution framework to make loosely coupled programming on petascale systems a practical and useful programming model. This work studies and measures the performance factors involved in applying…