相关论文: Towards Universal Mesh Movement Networks

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Universal meshes have recently appeared in the literature as a compu- tationally efficient and robust paradigm for the generation of conforming simpli- cial meshes for domains with evolving boundaries. The main idea behind a univer- sal…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…

Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…

We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a background mesh to curvilinear ones that conform exactly to the…

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Pixel2Mesh (P2M) is a classical approach for reconstructing 3D shapes from a single color image through coarse-to-fine mesh deformation. Although P2M is capable of generating plausible global shapes, its Graph Convolution Network (GCN)…

Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge,…

Deep learning has shown significant value in medical image registration for motion correction, however, current techniques are either limited by the type and range of motion they can handle, or require iterative inference and/or retraining…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also…

The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes. Meshing functionals are discretized geometrically and…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

Collision-free motion generation in unknown environments is a core building block for robot manipulation. Generating such motions is challenging due to multiple objectives; not only should the solutions be optimal, the motion generator…

Mesh generation is a crucial step in numerical simulations, significantly impacting simulation accuracy and efficiency. However, generating meshes remains time-consuming and requires expensive computational resources. In this paper, we…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…