Related papers: The Numerics of VMEC++
Distributed data processing systems have advanced through models that expose more and more opportunities for concurrency within a computation. The scheduling of these increasingly sophisticated models has become the bottleneck for improved…
Multivariate time series forecasting requires simultaneously modeling temporal patterns and cross-variate dependencies. Channel-independent methods such as PatchTST excel at temporal modeling but ignore variable correlations, while pure…
Intrinsic functions are specialized functions provided by the compiler that efficiently operate on architecture-specific hardware, allowing programmers to write optimized code in a high-level language that fully exploits hardware features.…
3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, and nonlinear analytic theory [Kleiner et al, PPCF 61 084005…
Quantum Error Correction (QEC) is essential for building robust, fault-tolerant quantum computers; however, the decoding process often presents a significant computational bottleneck. Tesseract is a novel Most-Likely-Error (MLE) decoder for…
We overview the ensmallen numerical optimization library, which provides a flexible C++ framework for mathematical optimization of user-supplied objective functions. Many types of objective functions are supported, including general,…
Harmonic model predictive control (HMPC) is a model predictive control (MPC) formulation which displays several benefits over other MPC formulations, especially when using a small prediction horizon. These benefits, however, come at the…
Achieving fault-tolerant quantum computation (FTQC) demands simultaneous progress in physical qubit performance and quantum error correction (QEC). This work reviews and benchmarks experimental advancements towards FTQC across leading…
Recent development of real-time equilibrium code Equinox [1] using a fixed-point algorithm [2] allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code…
While memory corruption bugs stemming from the use of unsafe programming languages are an old and well-researched problem, the resulting vulnerabilities still dominate real-world exploitation today. Various mitigations have been proposed to…
Quantum error correction (QEC) is essential for building scalable quantum computers, but a lack of systematic, end-to-end evaluation methods makes it difficult to assess how different QEC codes perform under realistic conditions. The vast…
This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix…
We present the MultiWave C++-framework for adaptive numerical methods approximating hyperbolic balance laws. MultiWave has been designed as a computational laboratory where new mathematical concepts can be quickly implemented and tested. We…
As large language models (LLMs) continue to advance, the demand for higher quality and faster processing of long contexts across various applications is growing. KV cache is widely adopted as it stores previously generated key and value…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
Finding Minimum Energy Configurations (MECs) is essential in fields such as physics, chemistry, and materials science, as they represent the most stable states of the systems. In particular, identifying such MECs in multi-component alloys…
Vector quantization (VQ) transforms continuous image features into discrete representations, providing compressed, tokenized inputs for generative models. However, VQ-based frameworks suffer from several issues, such as non-smooth latent…
This work systematically investigates the performance of FORCE--$\alpha$ numerical fluxes within an arbitrary high order semidiscrete finite volume (FV) framework for hyperbolic partial differential equations (PDEs). Such numerical fluxes…
This paper proposes a constrained maximum likelihood estimator for sequential search models, using the MPEC (Mathematical Programming with Equilibrium Constraints) approach. This method enhances numerical accuracy while avoiding ad hoc…
The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…