Related papers: Super-resolving sparse observations in partial dif…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

Deep Convolutional Neural Networks (CNNs) for image classification successively alternate convolutions and downsampling operations, such as pooling layers or strided convolutions, resulting in lower resolution features the deeper the…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities. Commonly, the convolution operators couple features from all…

Super-resolution (SR) techniques based on deep learning have recently emerged as a promising approach to enhance the spatial resolution of computational fluid dynamics simulations while containing computational cost. In this paper, we…

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an…

Phenomenally successful in practical inference problems, convolutional neural networks (CNN) are widely deployed in mobile devices, data centers, and even supercomputers. The number of parameters needed in CNNs, however, are often large and…

We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

Learning powerful feature representations for image retrieval has always been a challenging task in the field of remote sensing. Traditional methods focus on extracting low-level hand-crafted features which are not only time-consuming but…

Convolutional neural networks (CNNs) depend on deep network architectures to extract accurate information for image super-resolution. However, obtained information of these CNNs cannot completely express predicted high-quality images for…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…