相关论文: A Neural Network Study of Blasius Equation

To reduce memory footprint and run-time latency, techniques such as neural network pruning and binarization have been explored separately. However, it is unclear how to combine the best of the two worlds to get extremely small and efficient…

In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data…

Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.

We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates the solution of the equation under the…

In this paper, we address the problem of data description using a Bayesian framework. The goal of data description is to draw a boundary around objects of a certain class of interest to discriminate that class from the rest of the feature…

The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets…

The current study is a pioneering work in presenting the boundary layer equations for the two-dimensional flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of partial differential equations is turned…

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

We propose an energy stable network (EStable-Net) for solving gradient flow equations. The EStable-Net enables decreasing of a discrete energy along the neural network, which is consistent with the property of the gradient flow equation.…

In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…

How to effectively approximate real-valued parameters with binary codes plays a central role in neural network binarization. In this work, we reveal an important fact that binarizing different layers has a widely-varied effect on the…

Neural network pruning is a highly effective technique aimed at reducing the computational and memory demands of large neural networks. In this research paper, we present a novel approach to pruning neural networks utilizing Bayesian…