Related papers: LogLatt: A computational library for the calculus …

We discuss an agent-based approach to proof design and implementation, which we call {\it Lemma Flow Diagram} (LFD). This approach is based on the multicut rule with $shared$ cuts. This approach is modular and easy to use, read and…

Mathematical reasoning is an important research direction in the field of artificial intelligence. This article proposes a novel multi tool application framework for mathematical reasoning, aiming to achieve more comprehensive and accurate…

We present Lyncs-API, a Python API for Lattice QCD applications currently under development. Lyncs aims to bring several widely used libraries for Lattice QCD under a common framework. Lyncs flexibly links to libraries for CPUs and GPUs in…

We propose using natural language outlines as a novel modality and interaction surface for providing AI assistance to developers throughout the software development process. An NL outline for a code function comprises multiple statements…

We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. First, we demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers,…

libact is a Python package designed to make active learning easier for general users. The package not only implements several popular active learning strategies, but also features the active-learning-by-learning meta-algorithm that assists…

Large language models (LLMs) were invented for natural language tasks such as translation, but they have proved that they can perform highly complex functions across domains. Additionally, they have been thought to develop new skills…

Large language models (LLMs) have demonstrated remarkable potential across numerous applications and have shown an emergent ability to tackle complex reasoning tasks, such as mathematical computations. However, even for the simplest…

QC Lab is an open-source Python package for QC dynamics simulations aimed to promote the development of QC algorithms, and their application to a wide variety of relevant model problems. It follows a modular design that facilitates…

The past two decades showed a rapid growing of physically-based modeling of fluids for computer graphics applications. In this area, a common top down approach is to model the fluid dynamics by Navier-Stokes equations and apply a numerical…

Learning computational fluid dynamics (CFD) traditionally relies on computationally intensive simulations of the Navier-Stokes equations. Recently, large language models (LLMs) have shown remarkable pattern recognition and reasoning…

A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…

This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element…

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…

We comment on the role and impact of lattice fluid dynamics on the general landscape of computational fluid dynamics. Starting from the historical development of Lattice Gas Cellular Automata, we move on to a cursory appraisal of the main…

The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…

In the article we outline the set of Matlab functions that enable the computation of elliptic Integrals and Jacobian elliptic functions for real arguments. Correctness, robustness, efficiency and accuracy of the functions are discussed in…

DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and…

A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and…

MathLink is Wolfram Research's protocol for communicating with the Mathematica Kernel and is used extensively in their own Notebook Frontends. The Mathematica Book insinuates that linking C programs with MathLink is straightforward but in…