Related papers: Least-Squares Neural Network (LSNN) Method For Sca…

This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the…

Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent…

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the…

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined…

The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…

For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…

A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…

Recently deep convolutional neural networks have achieved significant success in salient object detection. However, existing state-of-the-art methods require high-end GPUs to achieve real-time performance, which makes them hard to adapt to…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

Underwater communication signals typically suffer from distortion due to motion-induced Doppler. Especially in shallow water environments, recovering the signal is challenging due to the time-varying Doppler effects distorting each path…

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…

The channel estimation (CE) in wireless receivers is one of the most critical and computationally complex signal processing operations. Recently, various works have shown that the deep learning (DL) based CE outperforms conventional minimum…

While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn…

We propose a discontinuous least squares finite element method for solving the Helmholtz equation. The method is based on the L2 norm least squares functional with the weak imposition of the continuity across the interior faces as well as…

The echo state network (ESN) is a special type of recurrent neural networks for processing the time-series dataset. However, limited by the strong correlation among sequential samples of the agent, ESN-based policy control algorithms are…

This work proposes a novel neural network architecture, called the Dynamically Controlled Recurrent Neural Network (DCRNN), specifically designed to model dynamical systems that are governed by ordinary differential equations (ODEs). The…

Recurrent stochastic configuration networks (RSCNs) have shown great potential in modelling nonlinear dynamic systems with uncertainties. This paper presents an RSCN with hybrid regularization to enhance both the learning capacity and…

In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…

The linear regression (LR) method offers the advantage that optimal parameters can be calculated relatively easily, although its representation capability is limited than that of the deep learning technique. To improve deep reinforcement…

Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to…