Related papers: The Numerics of VMEC++
This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson…
The increasing complexity of autonomous systems has driven a shift to integrated heterogeneous SoCs with real-time and safety demands. Ensuring deterministic WCETs and low-latency for critical tasks requires minimizing interference on…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a…
Modern microprocessors are equipped with Single Instruction Multiple Data (SIMD) or vector instructions which expose data level parallelism at a fine granularity. Programmers exploit this parallelism by using low-level vector intrinsics in…
The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…
Stochastic computing (SC) has emerged as a promising computing paradigm for neural acceleration. However, how to accelerate the state-of-the-art Vision Transformer (ViT) with SC remains unclear. Unlike convolutional neural networks, ViTs…
MONKES is a new neoclassical code for the evaluation of monoenergetic transport coefficients in stellarators. By means of a convergence study and benchmarks with other codes, it is shown that MONKES is accurate and efficient. The…
Vision encoders serve as the cornerstone of multimodal understanding. Single-encoder architectures like CLIP exhibit inherent constraints in generalizing across diverse multimodal tasks, while recent multi-encoder fusion methods introduce…
With the skyrocketing costs of GPUs and their virtual instances in the cloud, there is a significant desire to use CPUs for large language model (LLM) inference. KV cache update, often implemented as allocation, copying, and in-place…
We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is…
The numerical study of relativistic magnetohydrodynamics (MHD) plays a crucial role in high-energy astrophysics, but unfortunately is computationally demanding, given the complex physics involved (high Lorentz factor flows, extreme…
In this work, we introduce three algorithmic improvements to reduce the cost and improve the scaling of orbital space variational Monte Carlo (VMC). First, we show that by appropriately screening the one- and two-electron integrals of the…
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular,…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Resource-management tasks in modern operating and distributed systems continue to rely primarily on hand-designed heuristics for tasks such as scheduling, caching, or active queue management. Designing performant heuristics is an expensive,…
We present the new recombination code HYREC-2, holding the same accuracy as the state-of-the-art codes HYREC and COSMOREC and, at the same time, surpassing the computational speed of the code RECFAST commonly used for CMB-anisotropy data…
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…
Efficiently solving the Shortest Vector Problem (SVP) in two-dimensional lattices holds practical significance in cryptography and computational geometry. While simpler than its high-dimensional counterpart, two-dimensional SVP motivates…