Related papers: Geometry aware inference of steady state PDEs usin…

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…

Recent advances in integrating positional and structural encodings (PSEs) into graph neural networks (GNNs) have significantly enhanced their performance across various graph learning tasks. However, the general applicability of these…

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…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…

The accurate prediction of changes in protein stability under multiple amino acid substitutions is essential for realising true in-silico protein re-design. To this purpose, we propose improvements to state-of-the-art Deep learning (DL)…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…

Neural operators have demonstrated considerable effectiveness in accelerating the solution of time-dependent partial differential equations (PDEs) by directly learning governing physical laws from data. However, for PDEs governed by…

Geometric deep learning has recently gained significant attention in the computer vision community for its ability to capture meaningful representations of data lying in a non-Euclidean space. To this end, we propose E2E-GNet, an end-to-end…

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

Real-world geometry and 3D vision tasks are replete with challenging symmetries that defy tractable analytical expression. In this paper, we introduce Neural Isometries, an autoencoder framework which learns to map the observation space to…

We integrate two powerful ideas, geometry and deep visual representation learning, into recurrent network architectures for mobile visual scene understanding. The proposed networks learn to "lift" and integrate 2D visual features over time…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

For numerical design, the development of efficient and accurate surrogate models is paramount. They allow us to approximate complex physical phenomena, thereby reducing the computational burden of direct numerical simulations. We propose…

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…

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…