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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…

Computer Vision and Pattern Recognition · Computer Science 2018-12-12 Yinghao Xu , Xin Dong , Yudian Li , Hao Su

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…

Machine Learning · Computer Science 2021-06-30 Li-Ping Liu , Ruiyuan Gu , Xiaozhe Hu

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…

Numerical Analysis · Mathematics 2018-06-14 Yating Wang , Siu Wun Cheung , Eric T. Chung , Yalchin Efendiev , Min Wang

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…

Machine Learning · Computer Science 2019-04-12 Leah Bar , Nir Sochen

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…

Machine Learning · Statistics 2020-10-27 Trung Trinh , Samuel Kaski , Markus Heinonen

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…

Symbolic Computation · Computer Science 2026-01-14 Louis Gaillard

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.

General Mathematics · Mathematics 2023-05-10 Kerry M. Soileau

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…

Pattern Formation and Solitons · Physics 2022-07-20 Shikun Cui , Zhen Wang , Jiaqi Han , Xinyu Cui

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…

Machine Learning · Computer Science 2016-02-26 Alireza Ghasemi , Hamid R. Rabiee , Mohammad T. Manzuri , M. H. Rohban

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…

Machine Learning · Computer Science 2025-05-23 Valentin Villecroze , Yixin Wang , Gabriel Loaiza-Ganem

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…

Machine Learning · Computer Science 2025-07-11 David Boetius , Stefan Leue , Tobias Sutter

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…

Machine Learning · Computer Science 2023-05-23 Guy Lorberbom , Itai Gat , Yossi Adi , Alex Schwing , Tamir Hazan

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…

Fluid Dynamics · Physics 2016-09-08 Masood Khan , Mehwish Manzur , Masood ur Rahman

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…

Machine Learning · Computer Science 2022-09-30 Satya Borgohain , Klaus Ackermann , Ruben Loaiza-Maya

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,…

Numerical Analysis · Mathematics 2021-10-04 Guochang Lin , Pipi Hu , Fukai Chen , Xiang Chen , Junqing Chen , Jun Wang , Zuoqiang Shi

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.…

Machine Learning · Computer Science 2024-12-30 Yue Wu , Tianyu Jin , Chuqi Chen , Ganghua Fan , Yuan Lan , Luchan Zhang , Yang Xiang

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…

Fluid Dynamics · Physics 2021-01-26 Aaron B. Buhendwa , Stefan Adami , Nikolaus A. Adams

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…

Computer Vision and Pattern Recognition · Computer Science 2018-02-19 Lixue Zhuang , Yi Xu , Bingbing Ni , Hongteng Xu

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…

Machine Learning · Statistics 2023-08-07 Sunil Mathew , Daniel B. Rowe