Related papers: Pretrain Finite Element Method: A Pretraining and …
Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…
The inverse Stefan problem, as a typical phase-change problem with moving boundaries, finds extensive applications in science and engineering. Recent years have seen the applications of physics-informed neural networks (PINNs) to solving…
The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types…
Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…
We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed. PETGEM is an open-source and…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We show how to construct the deep neural network (DNN) expert to predict quasi-optimal $hp$-refinements for a given computational problem. The main idea is to train the DNN expert during executing the self-adaptive $hp$-finite element…
The Phase Extraction Neural Network (PhENN) is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through…
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…
State-of-the-art semantic segmentation methods require sufficient labeled data to achieve good results and hardly work on unseen classes without fine-tuning. Few-shot segmentation is thus proposed to tackle this problem by learning a model…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
We study a family of $H^m$-conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of $2m$-th order partial differential equations in $\mathbb{R}^d$ for any $m,d…
Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g.,…
This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…
With the rise of cloud-edge collaboration, recommendation services are increasingly trained in distributed environments. Federated Recommendation (FR) enables such multi-end collaborative training while preserving privacy by sharing model…
Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…