Related papers: Compression challenges in large scale PDE solvers

Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…

Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptability but lacking spectral constraints, and spectral-based…

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…

To solve nonlinear partial differential equations (PDEs) is one of the most common but important tasks in not only basic sciences but also many practical industries. We here propose a quantum variational (QuVa) PDE solver with the aid of…

A key aspect of learned partial differential equation (PDE) solvers is that the main cost often comes from generating training data with classical solvers rather than learning the model itself. Another is that there are clear axes of…

Today's exponentially increasing data volumes and the high cost of storage make compression essential for the Big Data industry. Although research has concentrated on efficient compression, fast decompression is critical for analytics…

Image compression has been a frequent topic of presentations at ADASS. Compression is often viewed as just a technique to fit more data into a smaller space. Rather, the packing of data - its "density" - affects every facet of local data…

Context-aware compression techniques have gained increasing attention as model sizes continue to grow, introducing computational bottlenecks that hinder efficient deployment. A structured encoding approach was proposed to selectively…

We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…

Sparse matrices are the key ingredients of several application domains, from scientific computation to machine learning. The primary challenge with sparse matrices has been efficiently storing and transferring data, for which many sparse…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in in our revious publications where computability, in the rigorous sense of…

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

How can we compress language models without sacrificing accuracy? The number of compression algorithms for language models is rapidly growing to benefit from remarkable advances of recent language models without side effects due to the…

Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…

Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest…

This paper addresses the challenges of storage and communication costs for large-scale datasets in resource-constrained edge devices by proposing a novel dataset quantization approach to reduce intra-sample redundancy. Unlike traditional…

Big data refers to large and complex data sets that, under existing approaches, exceed the capacity and capability of current compute platforms, systems software, analytical tools and human understanding. Numerous lessons on the scalability…