Related papers: Why geometric integration?
Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved),…
Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…
Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…
Modern 3D computer vision leverages learning to boost geometric reasoning, mapping image data to classical structures such as cost volumes or epipolar constraints to improve matching. These architectures are specialized according to the…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
Over the last ten years, the realm of Artificial Intelligence (AI) has experienced an explosion of revolutionary breakthroughs, transforming what seemed like a far-off dream into a reality that is now deeply embedded in our everyday lives.…
We are studying Runge-Kutta methods along complex paths of integration from a geometric point of view. Thereby we derive special complex time grids, which applied to the problem of integrating a linear autonomous system of ordinary…
Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…
Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…
The success of modern Artificial Intelligence (AI) technologies depends critically on the ability to learn non-linear functional dependencies from large, high dimensional data sets. Despite recent high-profile successes, empirical evidence…
A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and…
Researchers and practitioners across many disciplines have recently adopted computational notebooks to develop, document, and share their scientific workflows - and the GIS community is no exception. This chapter introduces computational…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…
Graph neural networks (GNNs) have received great attention due to their success in various graph-related learning tasks. Several GNN frameworks have then been developed for fast and easy implementation of GNN models. Despite their…
Since its introduction, 3D Gaussian Splatting (3DGS) has rapidly transformed the landscape of 3D scene representations, inspiring an extensive body of associated research. Follow-up work includes analyses and contributions that enhance the…
Geospatial Knowledge Graphs (GeoKGs) model geoentities (e.g., places and natural features) and spatial relationships in an interconnected manner, providing strong knowledge support for geographic applications, including data retrieval,…
Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…
Graph Neural Networks (GNNs) have emerged as effective tools for learning tasks on graph-structured data. Recently, Graph-Informed (GI) layers were introduced to address regression tasks on graph nodes, extending their applicability beyond…