相关论文: An End-to-End Deep Learning Method for Solving Non…

While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…

We consider unsupervised cell nuclei segmentation in this paper. Exploiting the recently-proposed unpaired image-to-image translation between cell nuclei images and randomly synthetic masks, existing approaches, e.g., CycleGAN, have…

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

We present an adaptive variational procedure for unstructured meshes to capture fluid-fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen-Cahn…

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

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…

Continual Learning (CL) aims to enable models to sequentially learn multiple tasks without forgetting previous knowledge. Recent studies have shown that optimizing towards flatter loss minima can improve model generalization. However,…

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality.…

We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator…

Training a deep neural network with the outputs of selected layers satisfying linear constraints is required in many contemporary data-driven applications. While this can be achieved by incorporating projection layers into the neural…

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the…

Recent achievements in end-to-end deep learning have encouraged the exploration of tasks dealing with highly structured data with unified deep network models. Having such models for compressing audio signals has been challenging since it…

Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution…

The atomistic-to-continuum (a/c) coupling methods, also known as the quasicontinuum (QC) methods, are a important class of concurrent multisacle methods for modeling and simulating materials with defects. The a/c methods aim to balance the…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…