arXiv subjects

Gabriel Kosmacher

Publications and source records attributed to Gabriel Kosmacher.

4 recordsLinked to original sources

arXiv2026

Interactive Debugger for Performance Portable Python HPC Kernels

We propose PKDB, the first interactive debugger for GPU and multithreaded low-level kernels written in Python. Python is widely used in high performance computing (HPC), with frameworks such as PyKokkos translating Python-embedded domain-specific languages to native code that runs across OpenMP-threaded CPUs and various GPUs. Yet interactive debugging support for such code is absent: developers resort to print statements, framework-specific assertions, or CPU-only execution, the last of which requires altering the program or its data and can mask device-specific bugs. PKDB enables standard interactive debugging like breakpoints, stepping, and variable inspection while preserving actual on-device execution without source modification. Beyond these fundamentals, PKDB introduces two advanced capabilities that exploit the dynamic nature of Python and PyKokkos: (i) Live code evaluation, which lets developers execute arbitrary Python expressions or entire kernels in the middle of a paused kernel without restarting the process; (ii) Kernel call site substitution, which allows an actively running kernel to be updated and reloaded on the fly, so only the kernel is recompiled and re-executed without restarting the application. Our performance evaluation on Intel, AMD, and NVIDIA CPUs, and NVIDIA and AMD GPUs shows that PKDB introduces limited overhead and is practical for everyday use while introducing critical debugging features to the Python HPC ecosystem.

cs.DC↗

arXiv2026

A Performance Portable Matrix Free Dense MTTKRP in GenTen

We extend the GenTen tensor decomposition package by introducing an accelerated dense matricized tensor times Khatri-Rao product (MTTKRP), the workhorse kernel for canonical polyadic (CP) tensor decompositions, that is portable and performant on modern CPU and GPU architectures. In contrast to the state-of-the-art matrix multiply based MTTKRP kernels used by Tensor Toolbox, TensorLy, etc., that explicitly form Khatri-Rao matrices, we develop a matrix-free element-wise parallelization approach whose memory cost grows with the rank R like the sum of the tensor shape O(R(n+m+k)), compared to matrix-based methods whose memory cost grows like the product of the tensor shape O(R(mnk)). For the largest problem we study, a rank 2000 MTTKRP, the smaller growth rate yields a matrix-free memory cost of just 2% of the matrix-based methods, a 50x improvement. In practice, the reduced memory impact means our matrix-free MTTKRP can compute a rank 2000 tensor decomposition on a single NVIDIA H100 instead of six H100s using a matrix-based MTTKRP. We also compare our optimized matrix-free MTTKRP to baseline matrix-free implementations on different devices, showing a 2x single-device speedup on an Intel 8480+ CPU, an 11x speedup on an NVIDIA H100 GPU and a 6x speedup on an AMD MI300A GPU. In addition to numerical results, we provide fine grained performance models for an ideal multi-level cache machine, compare analytical performance predictions to empirical results, and provide a motivated heuristic selection for selecting an algorithmic hyperparameter.

cs.MS↗

arXiv2026

A performance portable fast Ewald summation for Stokes flow

We present GPU algorithms for Ewald summation methods for accelerating N-body Stokes flow problems in periodic domains. Like most N-body codes, Ewald sums use a near-field/far-field decomposition. The near field involves particle-to-particle (P2P) interactions. The far field primarily involves particle-to-grid (P2G) and grid-to-particle (G2P) interactions, as well as Fast Fourier Transforms. For each interaction, we investigate several algorithmic variants. Our implementation uses PyKokkos, a Python interface for the Kokkos C++ parallel programming framework, which supports portability to AMD/NVIDIA GPU and ARM/x86 CPU architectures. Double and single-precision numerical results, alongside analytical performance models, confirm the efficiency of our algorithms on AMD and NVIDIA GPU and on ARM and AMD CPU architectures. The P2P interaction achieves around 73% compute efficiency on NVIDIA H200, 84% on NVIDIA A100, 60% on AMD MI300, 52% on Grace CPU, and 68% on AMD Epyc CPU. A straightforward implementation of the P2G kernel can become a computational bottleneck. We introduce a novel P2G algorithm that achieves up to 16$\times$ speedup compared to a baseline GPU implementation. The overall Ewald sum code processes approximately 8 million particles per second on a H200 GPU, and about a half-million particles per second on a Grace CPU, for nine digits of accuracy. We also perform a multi-GPU weak scaling test on up to 256 million particles (64 GPUs) that shows bounded communication cost for all stages except the all-to-all particle sorting, which can be reduced to neighbor communication in the relevant time-stepping regime.

math.NA↗

arXiv2023

Packing Densities of Delzant and Semitoric Polygons

Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing which fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four.

math.SG↗