subject

cs.MS

cs.MS: explore 27 source-linked works published from 2022 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2026

Code Generation for Near-Roofline Finite Element Actions on GPUs from Symbolic Variational Forms

We present a novel parallelization strategy for evaluating Finite Element Method (FEM) variational forms on GPUs, focusing on those that are expressible through the Unified Form Language (UFL) on simplex meshes. We base our approach on code transformations, wherein we construct a space of scheduling candidates and rank them via a heuristic cost model to effectively handle the large diversity of computational workloads that can be expressed in this way. We present a design of a search space to which the cost model is applied, along with an associated pruning strategy to limit the number of configurations that need to be empirically evaluated. The goal of our design is to strike a balance between the device's latency-hiding capabilities and the amount of state space, a key factor in attaining near-roofline performance. To make our work widely available, we have prototyped our parallelization strategy within the Firedrake framework, a UFL-based FEM solver. We evaluate the performance of our parallelization scheme on three generations of Nvidia GPUs, specifically the H200, Titan V and Tesla K40c, across a range of operators commonly used in applications, including fluid dynamics, wave propagation, and structural mechanics, in 2D and 3D geometries. Our results demonstrate that our proposed algorithm achieves more than $50\%$ roofline performance in $60\%$ of the test cases.

cs.DC↗

arXiv2026

Learning to Optimize by Differentiable Programming

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.

cs.MS↗

arXiv2026

Matrix-Aware Proper Scoring Rules and Significance Testing for Correlation and Covariance Forecasts in Python

Forecasting a correlation or covariance matrix is common in risk management and portfolio construction, but evaluating such a forecast correctly is not routine: naive matrix-comparison metrics are not proper scoring rules, walk-forward evaluation windows are easy to overlap with the estimation window in ways that silently leak information, and significance testing on serially dependent forecast-error sequences needs machinery few analysts implement from scratch. corrscore is a Python package that provides matrix-aware implementations of two established proper scoring rules for this setting -- the energy score and the variogram score -- dispatched across a closed-form tractability spectrum (point, discrete-mixture, and isotropic-Gaussian-mixture forecasts are scored exactly; a general Monte Carlo ensemble falls back to sampling), a geometry-aware variant of the variogram score built from the affine-invariant distance on the correlation manifold, a zero-overlap-by-construction walk-forward backtest harness, and a bundled significance-testing suite (circular block bootstrap, the Diebold-Mariano test, and the Model Confidence Set). We describe the package's design, its point of departure from the existing scoringRules and properscoring packages, and walk through a complete worked example.

stat.ME↗

arXiv2026

Fast Relax-and-Round Unit Commitment with Economic Horizons

The US energy system is increasingly under pressure to serve expanding data loads and to accommodate a larger number of generating units with varying technologies and own- ership structures. Therefore, developing new unit commitment methods remains a priority for reliable and affordable grid operations. We expand our novel computational method for unit commitment (UC) to include ramping constraints and long- horizon planning and provide a theoretical bound on its error. We introduce a fast novel algorithm to commit hydro-generators. We solve problems with thousands of generators at 5-minute market intervals. We show that our method can solve UC problems with over 20,000 generators in approximately 10 seconds on commodity hardware and that an increased planning horizon leads to sizable operational cost savings. We attain this runtime improvement by introducing a heuristic tailored for UC problems. Our method can be implemented using existing continuous optimization solvers and adapted for different applications. We prove a bound on the error of these solvers and show that it vanishes (in relative terms) as the problem becomes larger. We also introduce a fast and accurate hydro UC algorithm. Combined, these algorithms would allow an operator to make horizon-aware economic decisions for large systems with hydro units.

math.OC↗

arXiv2026

Performance Evaluation of Fast Fourier Transforms on Emerging RISC-V Hardware with Vector Extension Support

This manuscript presents a performance evaluation of Fast Fourier Transform (FFT) implementations on emerging processors supporting the RISC-V Vector Extension (RVV 1.0). By introducing juFFTe, a light-weight high-performance library for discrete Fourier transforms, it is demonstrated how effective vectorization of performance-critical FFT kernels can be achieved on RVV-enabled hardware. Comprehensive benchmarks on three RVV 1.0-ready processors, the SiFive X280, the X100 core of the SpacemiT K3 and the C920v2 core of the Sophon SG2044, reveal substantial performance improvements of juFFTe (https://github.com/FZJ-JSC/juFFTe) over the widely used FFTW3 library. Although RVV-enabled platforms show promising results at this stage of development, a comparison with AMD's Zen 5 architecture indicates that RISC-V needs further maturing to reach the performance of established micro-architectures.

cs.MS↗

arXiv2026

A GPU-Accelerated Blocked Adaptive Randomized Range Finder Based on an Implicit Householder QR Decomposition

Low-rank methods can reduce the memory and computational requirements of deep neural network training in approaches such as GaLore. Randomized range finders offer an attractive alternative to singular value decompositions, particularly when the required rank is determined adaptively from a prescribed approximation tolerance. We introduce a blocked adaptive randomized range finder based on an implicit Householder QR decomposition and an optimized hybrid CPU--GPU implementation. The proposed method avoids explicit reorthogonalization. Numerical experiments show that it preserves orthogonality and approximation accuracy in regimes where block Gram--Schmidt without reorthogonalization becomes unstable. The blocked formulation exposes matrix--matrix operations and enables overlap of CPU panel factorization with GPU updates. On an NVIDIA GH200, the overlapped implementation reduces the runtime for the largest tested matrix from 9.91 seconds on the CPU to 0.407 seconds. The method provides a stable and efficient building block for low-rank approximation on heterogeneous systems with applications in computational science and engineering.

math.NA↗

arXiv2025

Compiler-supported reduced precision and AoS-SoA transformations for heterogeneous hardware

This study evaluates AoS-to-SoA transformations over reduced-precision data layouts for a particle simulation code on several GPU platforms: We hypothesize that SoA fits particularly well to SIMT, while AoS is the preferred storage format for many Lagrangian codes. Reduced-precision (below IEEE accuracy) is an established tool to address bandwidth constraints, although it remains unclear whether AoS and precision conversions should execute on a CPU or be deployed to a GPU if the compute kernel itself must run on an accelerator. On modern superchips where CPUs and GPUs share (logically) one data space, it is also unclear whether it is advantageous to stream data to the accelerator prior to the calculation, or whether we should let the accelerator transform data on demand, i.e.~work in-place logically. We therefore introduce compiler annotations to facilitate such conversions and to give the programmer the option to orchestrate the conversions in combination with GPU offloading. For some of our compute kernels of interest, Nvidia's G200 platforms yield a speedup of around 2.6 while AMD's MI300A exhibits more robust performance yet profits less. We assume that our compiler-based techniques are applicable to a wide variety of Lagrangian codes and beyond.

cs.PL↗

arXiv2026

Ozaki Scheme II: A GEMM-oriented emulation of floating-point matrix multiplication using an integer modular technique

This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware architectures. The Ozaki scheme is a well-established GEMM-based emulation method for matrix multiplication, wherein input matrices are decomposed into several low-precision components to ensure that the resulting matrix product is computed exactly through numerical operations. This study proposes a novel GEMM-based emulation method for matrix multiplication that leverages the Chinese Remainder Theorem. The proposed method inherits the computational efficiency of highly optimized GEMM routines and further enables control over the number of matrix multiplications, which can enhance computational accuracy. We present numerical experiments featuring INT8 Tensor Core operations on GPUs and FP64 arithmetic on CPUs as case studies. The results demonstrate that FP64 emulation using the proposed method achieves performance levels of up to 7.4 to 9.8 TFLOPS on the NVIDIA RTX 4090 and 56.6 to 80.2 TFLOPS on the NVIDIA GH200, exceeding the measured performance of native FP64 arithmetic. Furthermore, for FP64 computations on CPUs, the proposed method achieved up to a 2.3x speedup in emulating quadruple-precision arithmetic compared to the conventional Ozaki scheme.

cs.MS↗

arXiv2022

DIRECTGO: A new DIRECT-type MATLAB toolbox for derivative-free global optimization

In this work, we introduce DIRECTGO, a new MATLAB toolbox for derivative-free global optimization. DIRECTGO collects various deterministic derivative-free DIRECT-type algorithms for box-constrained, generally-constrained, and problems with hidden constraints. Each sequential algorithm is implemented in two ways: using static and dynamic data structures for more efficient information storage and organization. Furthermore, parallel schemes are applied to some promising algorithms within DIRECTGO. The toolbox is equipped with a graphical user interface (GUI), ensuring the user-friendly use of all functionalities available in DIRECTGO. Available features are demonstrated in detailed computational studies using a comprehensive DIRECTGOLib v1.0 library of global optimization test problems. Additionally, eleven classical engineering design problems illustrate the potential of DIRECTGO to solve challenging real-world problems. Finally, the appendix gives examples of accompanying MATLAB programs and provides a synopsis of its use on the test problems with box and general constraints.

math.OC↗

Compare source metadata on this page

Work	Published	Source identifier	Source
Code Generation for Near-Roofline Finite Element Actions on GPUs from Symbolic Variational Forms	2026-08-30	2506.17471	arxiv
Learning to Optimize by Differentiable Programming	2026-08-30	2601.16510	arxiv
Matrix-Aware Proper Scoring Rules and Significance Testing for Correlation and Covariance Forecasts in Python	2026-08-30	2609.01648	arxiv
Fast Relax-and-Round Unit Commitment with Economic Horizons	2026-08-28	2603.15934	arxiv
Performance Evaluation of Fast Fourier Transforms on Emerging RISC-V Hardware with Vector Extension Support	2026-08-28	2608.28076	arxiv
A GPU-Accelerated Blocked Adaptive Randomized Range Finder Based on an Implicit Householder QR Decomposition	2026-08-28	2608.28941	arxiv
Compiler-supported reduced precision and AoS-SoA transformations for heterogeneous hardware	2025-12-05	2512.05516	arxiv
Ozaki Scheme II: A GEMM-oriented emulation of floating-point matrix multiplication using an integer modular technique	2026-09-16	2504.08009	arxiv
DIRECTGO: A new DIRECT-type MATLAB toolbox for derivative-free global optimization	2022-04-28	2107.02205	arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.