相关论文: Uniform error estimates for artificial neural netw…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

The demand for high speed data transmission has increased rapidly, leading to advanced optical communication techniques. In the past few years, multiple equalizers based on neural network (NN) have been proposed to recover signal from…

Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture…

This study evaluates the efficacy of two machine learning (ML) techniques, namely artificial neural networks (ANN) and gene expression programming (GEP) that use data-driven modeling to predict wall pressure spectra (WPS) underneath…

The use of neural networks to solve differential equations, as an alternative to traditional numerical solvers, has increased recently. However, error bounds for the obtained solutions have only been developed for certain equations. In this…

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed…

The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…

Autoregressive Neural Networks (ANN) have been recently proposed as a mechanism to improve the efficiency of Monte Carlo algorithms for several spin systems. The idea relies on the fact that the total probability of a configuration can be…

In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…

The isothermal gas sphere is a particular type of Lane-Emden equation and is used widely to model many problems in astrophysics like stars, star clusters, and the formation of galaxies. In this paper, we present a computational scheme to…

As a potential alternative for implementing the large number of multiplications in convolutional neural networks (CNNs), approximate multipliers (AMs) promise both high hardware efficiency and accuracy. However, the characterization of…

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to…

The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here we outline a new paradigm for deriving energy functions of hyperdimensional molecular…

With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…