Related papers: Towards Universal Mesh Movement Networks

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…

In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…

Motion generation is a cornerstone of computer graphics, animation, gaming, and robotics, enabling the creation of realistic and varied character movements. A significant limitation of existing methods is their reliance on specific skeletal…

In this work, we bridge the gap between recent pose estimation and tracking work to develop a powerful method for robots to track objects in their surroundings. Motion-Nets use a segmentation model to segment the scene, and separate…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…

Numerical simulation is indispensable in industrial design processes. It can replace expensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement,…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, to efficiently route information. In MNNs, information is propagated between neurons throughout a state transition…

Most of the recent deep learning-based 3D human pose and mesh estimation methods regress the pose and shape parameters of human mesh models, such as SMPL and MANO, from an input image. The first weakness of these methods is an appearance…

Mixture-of-Expert (MoE) models outperform conventional models by selectively activating different subnets, named experts, on a per-token basis. This gated computation generates dynamic communications that cannot be determined beforehand,…

We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T…

Neural operators, serving as physics surrogate models, have recently gained increased interest. With ever increasing problem complexity, the natural question arises: what is an efficient way to scale neural operators to larger and more…

We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information.…

Fast and efficient motion planning algorithms are crucial for many state-of-the-art robotics applications such as self-driving cars. Existing motion planning methods become ineffective as their computational complexity increases…

Moving mesh methods are designed to redistribute a mesh in a regular way. This applied problem can be considered to overlap with the problem of finding a diffeomorphic mapping between density measures. In applications, an off-the-shelf grid…

Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…

An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…