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Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Modeling physical systems is an essential skill for a control engineer, since it enables to achieve a deep understanding of their dynamic behavior and, consequently, the development of effective control strategies. The first part of this…

Feature transformation methods aim to find an optimal mathematical feature-feature crossing process that generates high-value features and improves the performance of downstream machine learning tasks. Existing frameworks, though designed…

We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it…

Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…

This paper presents the Embedding Pose Graph (EPG), an innovative method that combines the strengths of foundation models with a simple 3D representation suitable for robotics applications. Addressing the need for efficient spatial…

Computationally weak systems and demanding graphical applications are still mostly dependent on linear blendshapes for facial animations. The accompanying artifacts such as self-intersections, loss of volume, or missing soft tissue…

The multi-scale information among the whole slide images (WSIs) is essential for cancer diagnosis. Although the existing multi-scale vision Transformer has shown its effectiveness for learning multi-scale image representation, it still…

In the trend of hybrid Artificial Intelligence techniques, Physical-Informed Machine Learning has seen a growing interest. It operates mainly by imposing data, learning, or architecture bias with simulation data, Partial Differential…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

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…

Tensegrity robots are composed of rigid struts and flexible cables. They constitute an emerging class of hybrid rigid-soft robotic systems and are promising systems for a wide array of applications, ranging from locomotion to assembly. They…

Large Language Models (LLMs) have achieved impressive performance in text understanding and have become an essential tool for building smart assistants. Originally focusing on text, they have been enhanced with multimodal capabilities in…

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these…

Graph Neural Networks (GNNs) have gained significant traction for simulating complex physical systems, with models like MeshGraphNet demonstrating strong performance on unstructured simulation meshes. However, these models face several…

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to…

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…