Related papers: MP users guide
Simulations with high accuracy are an essential part of scientific research to accelerate the innovation process. They are especially useful for finding novel approaches or optimizing existing methods. Today, powerful software tools are…
Mirror-prox (MP) is a well-known algorithm to solve variational inequality (VI) problems. VI with a monotone operator covers a large group of settings such as convex minimization, min-max or saddle point problems. To get a convergent…
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…
We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…
MPI collective operations provide a standardized interface for performing data movements within a group of processes. The efficiency of collective communication operations depends on the actual algorithm, its implementation, and the…
Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…
GPUs and other accelerators are increasingly used for scientific computing. In the future, we want to add GPU support to parallel adaptive mesh refinement (AMR) codes written in Fortran. To understand which changes are necessary to obtain…
Universal machine-learned interatomic potentials (U-MLIPs) have demonstrated broad applicability across diverse atomistic systems but often require fine-tuning to achieve task-specific accuracy. While the number of available U-MLIPs and…
The article considers linear functions of many (n) variables - multilinear polynomials (MP). The three-steps evaluation is presented that uses the minimal possible number of floating point operations for non-sparse MP at each step. The…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
Machine Translation (MT) and automatic MT evaluation have improved dramatically in recent years, enabling numerous novel applications. Automatic evaluation techniques have evolved from producing scalar quality scores to precisely locating…
We introduce Meta Prompting (MP), a framework that elevates the reasoning capabilities of large language models (LLMs) by focusing on the formal structure of a task rather than content-specific examples. We establish a theoretical…
We present a novel framework for designing multiplierless kernel machines that can be used on resource-constrained platforms like intelligent edge devices. The framework uses a piecewise linear (PWL) approximation based on a margin…
Parallel loops are an important part of OpenMP programs. Efficient scheduling of parallel loops can improve performance of the programs. The current OpenMP specification only offers three options for loop scheduling, which are insufficient…
Magnetic particle imaging (MPI) is an emerging imaging technique with many applications and a very active field of research. This app provides users with the opportunity to develop some intuition about the inner workings of MPI as it is…
Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…
Multilayer perceptron (MLP) is a class of networks composed of multiple layers of perceptrons, and it is essentially a mathematical function. Based on MLP, we develop a new numerical method to find the extrema of functionals. As…
Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…
We discuss the use of both MPI and OpenMP in the teaching of senior undergraduate and junior graduate classes in parallel programming. We briefly introduce the OpenMP standard and discuss why we have chosen to use it in parallel programming…