Related papers: HiDeNN-PGD: reduced-order hierarchical deep learni…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
Scientific applications produce vast amounts of data, posing grand challenges in the underlying data management and analytic tasks. Progressive compression is a promising way to address this problem, as it allows for on-demand data…
The introduction of Physics-informed Neural Networks (PINNs) has led to an increased interest in deep neural networks as universal approximators of PDEs in the solid mechanics community. Recently, the Deep Energy Method (DEM) has been…
In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…
In the present work a new set of differential equations for the Hopfield Neural Network (HNN) method were established by means of the Linear Extended Gateaux Derivative (LEGD). This new approach will be referred to as G\^ateaux-Hopfiel…
In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…
Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models,…
We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…
Both high-level and high-resolution feature representations are of great importance in various visual understanding tasks. To acquire high-resolution feature maps with high-level semantic information, one common strategy is to adopt dilated…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…
Deep neural networks (DNN) have achieved remarkable success in various fields, including computer vision and natural language processing. However, training an effective DNN model still poses challenges. This paper aims to propose a method…
This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
Traditional CNN models are trained and tested on relatively low resolution images (<300 px), and cannot be directly operated on large-scale images due to compute and memory constraints. We propose Patch Gradient Descent (PatchGD), an…
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.…
Conventional Convolutional neural networks (CNN) are trained on large domain datasets and are hence typically over-represented and inefficient in limited class applications. An efficient way to convert such large many-class pre-trained…