相关论文: General-domain FC-based shock-dynamics solver I: B…

We introduce a fast solver for the phase field crystal (PFC) and functionalized Cahn-Hilliard (FCH) equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov accelerated gradient descent…

Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method…

Deep Neural Networks (DNNs) are powerful tools that have shown extraordinary results in many scenarios, ranging from pattern recognition to complex robotic problems. However, their intricate designs and lack of transparency raise safety…

A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…

Nonlinearly stable flux reconstruction (NSFR) combines the key properties of provable nonlinear stability with the increased time step from energy-stable flux reconstruction. The NSFR scheme has been successfully applied to unsteady…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent…

Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary…

This paper proposes a data-driven graphical framework for the real-time search of risky cascading fault chains (FCs). While identifying risky FCs is pivotal to alleviating cascading failures, the complex spatio-temporal dependencies among…

The Fourier transform, an explicit decomposition method for visual signals, has been employed to explain the out-of-distribution generalization behaviors of Deep Neural Networks (DNNs). Previous studies indicate that the amplitude spectrum…

This paper introduces a novel neural network - flow completion network (FCN) - to infer the fluid dynamics, includ-ing the flow field and the force acting on the body, from the incomplete data based on Graph Convolution AttentionNetwork.…

This paper introduces a novel two-stream deep model based on graph convolutional network (GCN) architecture and feed-forward neural networks (FFNN) for learning the solution of nonlinear partial differential equations (PDEs). The model aims…

We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…

To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the…

We present a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods we (1) enclose the ensemble of scatterers in a domain bounded by an…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Recent advances in unsupervised domain adaptation (UDA) techniques have witnessed great success in cross-domain computer vision tasks, enhancing the generalization ability of data-driven deep learning architectures by bridging the domain…

Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with…

Solving partial differential equations (PDEs) is an important yet challenging task in fluid mechanics. In this study, we embed an improved Fourier series into neural networks and propose a physics-informed Fourier basis neural network…

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…