Related papers: An exploration to visualize finite element data wi…
Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide…
Scientific simulations and experimental measurements produce vast amounts of spatio-temporal data, yet extracting meaningful insights remains challenging due to high dimensionality, complex structures, and missing information. Traditional…
Using LLMs not to predict plans but to formalize an environment into the Planning Domain Definition Language (PDDL) has been shown to improve performance and control. While most existing methodology only applies to fully observable…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
We introduce a new abstraction for the representation and solution of multi-domain problems using finite element methods. This is an advance over previous work in that it achieves a single higher-level abstraction that represents…
Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However,…
We present the design and prototype implementation of a scientific visualization language called Zifazah for composing 3D visualizations of diffusion tensor magnetic resonance imaging (DT-MRI or DTI) data. Unlike existing tools allowing…
I present a new FITS viewer designed to explore 3D spectral line data (in particular HI) and assist with visual source extraction and analysis. Using the artistic software Blender, FRELLED can visualise even large (~600^3 voxels) data sets…
This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users.…
We present Firefly, a new browser-based interactive tool for visualizing 3D particle data sets. On a typical personal computer, Firefly can simultaneously render and enable real-time interactions with > ~10 million particles, and can…
We show that the DDR method can be interpreted as defining a computable consistent discrete $\mathrm{L}^2$ product on a conforming FES defined by PDEs. Without modifying the numerical method itself, this point of view provides an…
Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite element transformations in FInAT…
This work introduces VERSE, a methodology for analyzing and improving Vision-Language Models applied to Visually-rich Document Understanding by exploring their visual embedding space. VERSE enables the visualization of latent…
Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and engineering, mainly due to the "curse of dimensionality" in…
In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which…
Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…