Related papers: G-Adaptivity: optimised graph-based mesh relocatio…
Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…
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…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Graph Neural Networks (GNNs) have experienced rapid advancements in recent years due to their ability to learn meaningful representations from graph data structures. Federated Learning (FL) has emerged as a viable machine learning approach…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
We devise a graph attention network-based approach for learning a scene triangle mesh representation in order to estimate an image camera position in a dynamic environment. Previous approaches built a scene-dependent model that explicitly…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method…
Adaptive mesh refinement (AMR) offers a practical solution to reduce the computational cost and memory requirement of numerical simulations that use computational meshes. In this work, we introduce a novel smart methodology for adaptive…
In massive multi-input multi-output (MIMO) systems, the main bottlenecks of location- and orientation-assisted beam alignment using deep neural networks (DNNs) are large training overhead and significant performance degradation. This paper…
In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant…
An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
Exact subgraph matching on large-scale graphs remains a challenging problem due to high computational complexity and distributed system constraints. Existing GNN-based path embedding (GNN-PE) frameworks achieve efficient exact matching on…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…