Related papers: Analysis of three dimensional potential problems i…

Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively…

In this paper, an innovative multi-modal deep learning model is proposed to deeply integrate heterogeneous information from medical images and clinical reports. First, for medical images, convolutional neural networks were used to extract…

This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy…

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Dynamic dispatching is one of the core problems for operation optimization in traditional industries such as mining, as it is about how to smartly allocate the right resources to the right place at the right time. Conventionally, the…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…

We study the feasibility of data based machine learning applied to ultrasound tomography to estimate water-saturated porous material parameters. In this work, the data to train the neural networks is simulated by solving wave propagation in…

The use of multimodal imaging has led to significant improvements in the diagnosis and treatment of many diseases. Similar to clinical practice, some works have demonstrated the benefits of multimodal fusion for automatic segmentation and…

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…

We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

Deep learning is known to be data-hungry, which hinders its application in many areas of science when datasets are small. Here, we propose to use transfer learning methods to migrate knowledge between different physical scenarios and…

Considerable research has been devoted to deep learning-based predictive models for system prognostics and health management in the reliability and safety community. However, there is limited study on the utilization of deep learning for…

This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations, illustrated through twisted two-dimensional large-scale material systems. The deep potential molecular…