Related papers: The Numerics of VMEC++
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to…
This work proposes for the first time a novel optimization method for numerical algorithms, which takes advantages of machine learning frameworks PyTorch and TensorRT, leveraging their modularity, low development threshold, and automatic…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
Multi-dimensional arrays are ubiquitous in high-performance computing (HPC), but their absence from the C++ language standard is a long-standing and well-known limitation of their use for HPC. This paper describes the design and…
Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic…
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…
In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, we restrict our analysis to triangular meshes with hanging…
One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a B\'ezier surface based finite element method. This code produces a highly sparse…
A key aspect in the modelling of magnetohydrodynamic (MHD) equilibria in tokamak devices is having access to fast, accurate, and stable numerical simulation methods. There is an increasing demand for reliable methods that can be used to…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
Modern compilers rely on hand-crafted heuristics to guide optimization passes. These human-designed rules often struggle to adapt to the complexity of modern software and hardware and lead to high maintenance burden. To address this…
The STEP (Stability, Transport, Equilibrium, and Pedestal) integrated-modeling tool has been developed in OMFIT to predict stable, tokamak equilibria self-consistently with core-transport and pedestal calculations. STEP couples theory-based…
The recent progress in artificial intelligence has led to an ever-increasing usage of images and videos by machine analysis algorithms, mainly neural networks. Nonetheless, compression, storage and transmission of media have traditionally…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
HEP-Frame is a new C++ package designed to efficiently perform analyses of data sets from a very large number of events, like those available at the Large Hadron Collider (LHC) at CERN, Geneva. It mainly targets high performance servers and…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an…
In 2018, Yang et al. introduced a novel and effective approach, using maximum distance separable (MDS) codes, to mitigate the impact of elasticity in cloud computing systems. This approach is referred to as coded elastic computing. Some…