Related papers: Compression challenges in large scale PDE solvers
Today, with the growing demands of information storage and data transfer, data compression is becoming increasingly important. Data Compression is a technique which is used to decrease the size of data. This is very useful when some huge…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Data compression is a well-studied (and well-solved) problem in the setup of long coding blocks. But important emerging applications need to compress data to memory words of small fixed widths. This new setup is the subject of this paper.…
New directions in computing and algorithms has lead to some new applications that have tolerance to imprecision. Although, These applications are creating large volumes of data which exceeds the capability of today's computing systems.…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Partial Differential Equations (PDEs) describe several problems relevant to many fields of applied sciences, and their discrete counterparts typically involve the solution of sparse linear systems. In this context, we focus on the analysis…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
Deep models have recently emerged as promising tools to solve partial differential equations (PDEs), known as neural PDE solvers. While neural solvers trained from either simulation data or physics-informed loss can solve PDEs reasonably…
Data compression is widely used in contemporary column-oriented DBMSes to lower space usage and to speed up query processing. Pioneering systems have introduced compression to tackle the disk bandwidth bottleneck by trading CPU processing…
Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while…
Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
Deep learning accelerators efficiently train over vast and growing amounts of data, placing a newfound burden on commodity networks and storage devices. A common approach to conserve bandwidth involves resizing or compressing data prior to…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
This paper considers the problem of distributed source coding for a large network. A major obstacle that poses an existential threat to practical deployment of conventional approaches to distributed coding is the exponential growth of the…