Related papers: Developments in GRworkbench
Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems.…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Computer algebra programs are presented for application in general relativity, in electrodynamics, and in gauge theories of gravity. The mathematical formalism used is the calculus of exterior differential forms, the computer algebra system…
Numerical physics has gained a lot of importance in the last decade, its efficiency being motivated and sustained by the growth of computational power. This paper presents a concept that is to be developed in the next few years: OpenPh.…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…
Deep neural networks (DNNs) have shown remarkable performance improvements on vision-related tasks such as object detection or image segmentation. Despite their success, they generally lack the understanding of 3D objects which form the…
We develop the Mechanic package, which is a new numerical framework for dynamical astronomy. The aim of our software is to help in massive numerical simulations by efficient task management and unified data storage. The code is built on top…
Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
Deep networks have brought significant advances in robot perception, enabling to improve the capabilities of robots in several visual tasks, ranging from object detection and recognition to pose estimation, semantic scene segmentation and…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches…
Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree…