Related papers: Function space bases in the dune-functions module

Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software concepts and abstractions to handle the composition of function…

The dune-functions dune module introduces a new programmer interface for discrete and non-discrete functions. Unlike the previous interfaces considered in the existing dune modules, it is based on overloading operator(), and returning…

In this paper we present the new Dune-Python module which provides Python bindings for the Dune core, which is a C++ environment for solving partial differential equations. The aim of this new module is to firstly provide the general…

In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…

This is a survey on Anderson t-motives -- high-dimensional generalizations of Drinfeld modules. They are the functional field analogs of abelian varieties with multiplication by an imaginary quadratic field. We describe their lattices,…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…

Finite element (FE) analysis has the potential to offset much of the expensive experimental testing currently required to certify aerospace laminates. However, large numbers of degrees of freedom are necessary to model entire aircraft…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

In this paper, we introduce a novel non-linear activation function that spontaneously induces class-compactness and regularization in the embedding space of neural networks. The function is dubbed DOME for Difference Of Mirrored Exponential…

A brief introduction of the technical approach to model FTUs as an aggregate of cells, whose state transition dynamics are mathematically represented as port-hamiltonians or Differential Algebraic equations is presented. A python library…

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…

Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…

A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…

The focus of this paper is providing a description of the spaces of counting functions on free monoids and groups and of the Brooks space. These results have been obtained in an earlier publication, however we propose an alternative,…

We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…

Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…

Systematic expansion schemes in functional approaches require the inclusion of higher order vertices. These vertices are expanded in independent tensor bases with a rapidly increasing number of basis elements. Amongst the related tasks are…

This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted…