Related papers: Veamy: an extensible object-oriented C++ library f…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can be described with this tool and have many…
Language models (LMs) and their extension, vision-language models (VLMs), have achieved remarkable performance across various tasks. However, they still struggle with complex reasoning tasks that require multimodal or multilingual…
Advances in 3D generative AI have enabled the creation of physical objects from text prompts, but challenges remain in creating objects involving multiple component types. We present a pipeline that integrates 3D generative AI with…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
Vision-language models (VLMs) integrate visual and textual information, enabling a wide range of applications such as image captioning and visual question answering, making them crucial for modern AI systems. However, their high…
CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
We introduce VLM-Lens, a toolkit designed to enable systematic benchmarking, analysis, and interpretation of vision-language models (VLMs) by supporting the extraction of intermediate outputs from any layer during the forward pass of…
This work introduces Pressio, an open-source project aimed at enabling leading-edge projection-based reduced order models (ROMs) for large-scale nonlinear dynamical systems in science and engineering. Pressio provides model-reduction…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e., functions belonging to the kernel of the…
Persistent Memory (PMEM), also known as Non-Volatile Memory (NVM), can deliver higher density and lower cost per bit when compared with DRAM. Its main drawback is that it is typically slower than DRAM. On the other hand, DRAM has…
Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…
A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for arbitrary unstructured meshes and dynamic local Adaptive Mesh Refinement (AMR), as well as for two and three dimensional computation is developed. The…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
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…
The paper presents the project of an open source C/C++ library of analytical solutions to micromechanical fields within media with ellipsoidal heterogeneities. The solutions are based on Eshelby's stress-free, in general polynomial,…
In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we…