Related papers: An efficient way to assemble finite element matric…
Modern processor architectures, in addition to having still more cores, also require still more consideration to memory-layout in order to run at full capacity. The usefulness of most languages is deprecating as their abstractions,…
Probabilistic programming languages (PPLs) are a popular tool for high-level modelling across many fields. They provide a range of algorithms for probabilistic inference, which analyse models by learning their parameters from a dataset or…
SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software's sustainability. In this publication we solve this sustainability and…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
With the advent of automatic vectorization tools (e.g., JAX's $\texttt{vmap}$), writing multi-chain MCMC algorithms is often now as simple as invoking those tools on single-chain code. Whilst convenient, for various MCMC algorithms this…
Auto-vectorization is a fundamental optimization for modern compilers to exploit SIMD parallelism. However, state-of-the-art approaches still struggle to handle intricate code patterns, often requiring manual hints or domain-specific…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
Large Language Models (LLMs) excel in natural language processing tasks but pose significant computational and memory challenges for edge deployment due to their intensive resource demands. This work addresses the efficiency of LLM…
In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding…
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal…
State-of-the-art algorithms generate scattering amplitudes for high-energy physics at leading order for high-multiplicity processes as compiled code (in Fortran, C or C++). For complicated processes the size of these libraries can become…
Finite element methods require the composition of the global stiffness matrix from local finite element contributions. The composition process combines the computation of element stiffness matrices and their assembly into the global…
We introduce a high-performance virtual machine (VM) written in a numerically fast language like Fortran or C to evaluate very large expressions. We discuss the general concept of how to perform computations in terms of a VM and present…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
One of the key challenges arising when compilers vectorize loops for today's SIMD-compatible architectures is to decide if vectorization or interleaving is beneficial. Then, the compiler has to determine how many instructions to pack…
We introduce ReALLM, a novel approach for compression and memory-efficient adaptation of pre-trained language models that encompasses most of the post-training quantization and fine-tuning methods for a budget of <4 bits. Pre-trained…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…