Related papers: Tensor calculus with open-source software: the Sag…
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
Tensor networks (TNs) are a central computational tool in quantum science and artificial intelligence. However, the lack of unified software interface across tensor-computing frameworks severely limits the portability of TN applications,…
Significant progress has been made in scene understanding which seeks to build 3D, metric and object-oriented representations of the world. Concurrently, reinforcement learning has made impressive strides largely enabled by advances in…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…
The abstract mathematical theory of partial differential equations (PDEs) is formulated in terms of manifolds, scalar fields, tensors, and the like, but these algebraic structures are hardly recognizable in actual PDE solvers. The general…
Recent work has shown that Field-Programmable Gate Arrays (FPGAs) play an important role in the acceleration of Machine Learning applications. Initial specification of machine learning applications are often done using a high-level…
We present the first public release (v0.1) of the open-source GADGET Dataframe Library: gadfly. The aim of this package is to leverage the capabilities of the broader python scientific computing ecosystem by providing tools for analyzing…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology
A novel Python framework for Bayesian optimization known as GPflowOpt is introduced. The package is based on the popular GPflow library for Gaussian processes, leveraging the benefits of TensorFlow including automatic differentiation,…
We introduce ninfty, a header-only C++ library distributed under an MIT Open Source License designed for the study of enumeration problems arising in homotopical combinatorics. The ninfty repository moreover contains a folder with data…
Systems Engineering (SE) is the set of processes and documentation required for successfully realising large-scale engineering projects, but the classical approach is not a good fit for software-intensive projects, especially when the needs…
Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…
The Lattice Gauge Theory Hilbert space is divided into gauge-invariant sectors selected by the background charges. Such a projector can be directly embedded in a tensor network ansatz for gauge-invariant states as originally discussed in…
We present a newly developed software package which implements a wide range of routines frequently used in Weak Gravitational Lensing (WL). With the continuously increasing size of the WL scientific community we feel that easy to use…
We propose a new architecture for optimization modeling frameworks in which solvers are expressed as computation graphs in a framework like TensorFlow rather than as standalone programs built on a low-level linear algebra interface. Our new…
We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the…