Related papers: Why geometric integration?

Deep reinforcement learning (DRL) has empowered a variety of artificial intelligence fields, including pattern recognition, robotics, recommendation-systems, and gaming. Similarly, graph neural networks (GNN) have also demonstrated their…

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…

Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…

The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…

In recent times, the trend in very large scale integration (VLSI) industry is multi-dimensional, for example, reduction of energy consumption, occupancy of less space, precise result, less power dissipation, faster response. To meet these…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

Scaling deep learning models has been at the heart of recent revolutions in language modelling and image generation. Practitioners have observed a strong relationship between model size, dataset size, and performance. However,…

Heterogeneous graphs offer powerful data representations for traffic, given their ability to model the complex interaction effects among a varying number of traffic participants and the underlying road infrastructure. With the recent advent…

Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…

Gamification has been applied in software engineering to improve quality and results by increasing people's motivation and engagement. A systematic mapping has identified research gaps in the field, one of them being the difficulty of…

Depth completion is the task of generating a dense depth map given an image and a sparse depth map as inputs. It has important applications in various downstream tasks. In this paper, we present OGNI-DC, a novel framework for depth…

Context: The rapid emergence of generative AI (GenAI) tools has begun to reshape various software engineering activities. Yet, their adoption within agile environments remains underexplored. Objective: This study investigates how agile…

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…

Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

The task of data integration for multi-omics data has emerged as a powerful strategy to unravel the complex biological underpinnings of cancer. Recent advancements in graph neural networks (GNNs) offer an effective framework to model…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

Artificial Intelligence significantly enhances the visual art industry by analyzing, identifying and generating digitized artistic images. This review highlights the substantial benefits of integrating geometric data into AI models,…

How are new technologies like generative AI quickly adopted and used by executive and managerial leaders to create value in organizations? A survey of INSEAD's global alumni base revealed several intriguing insights into perceptions and…

Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most…