相关论文: Are Two Hidden Layers Still Enough for the Physics…

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential equations (PDEs). Within this landscape, network…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed…

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

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.…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…

Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…

As a promising framework for resolving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have received widespread attention from industrial and scientific fields. However, lack of expressive ability and…

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of…

Deep neural networks (DNNs) form the backbone of almost every state-of-the-art technique in the fields such as computer vision, speech processing, and text analysis. The recent advances in computational technology have made the use of DNNs…

Background: Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

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…

Training deep neural networks for scientific computing remains computationally expensive due to the slow formation of diverse feature representations in early training stages. Recent studies identify a staircase phenomenon in training…