Related papers: Adaptive deep density approximation for stochastic…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

In this work, we have proposed a generative model, called VAE-KRnet, for density estimation or approximation, which combines the canonical variational autoencoder (VAE) with our recently developed flow-based generative model, called KRnet.…

We introduce an adaptive sampling method for the Deep Ritz method aimed at solving partial differential equations (PDEs). Two deep neural networks are used. One network is employed to approximate the solution of PDEs, while the other one is…

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these…

An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester~(J. Comput. Phys., 553 (2026), 114743),…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

Controlling nonlinear stochastic dynamical systems involves substantial challenges when the dynamics contain unknown and unstructured nonlinear state-dependent terms. For such complex systems, deep neural networks can serve as powerful…

In this paper, we consider a numerical homogenization of the poroelasticity problem with stochastic properties. The proposed method based on the construction of the deep neural network (DNN) for fast calculation of the effective properties…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for…

Recently, optimal time variable learning in deep neural networks (DNNs) was introduced in arXiv:2204.08528. In this manuscript we extend the concept by introducing a regularization term that directly relates to the time horizon in discrete…

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…

Accurate prediction of public transit ridership is vital for efficient planning and management of transit in rapidly growing urban areas in Canada. Unexpected increases in passengers can cause overcrowded vehicles, longer boarding times,…

There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring…

Traffic flow forecasting is considered a critical task in the field of intelligent transportation systems. In this paper, to address the issue of low accuracy in long-term forecasting of spatial-temporal big data on traffic flow, we propose…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

In this paper, we propose a novel layer-adaptive weight-pruning approach for Deep Neural Networks (DNNs) that addresses the challenge of optimizing the output distortion minimization while adhering to a target pruning ratio constraint. Our…

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…

Dynamic DNN optimization techniques such as layer-skipping offer increased adaptability and efficiency gains but can lead to i) a larger memory footprint as in decision gates, ii) increased training complexity (e.g., with non-differentiable…

Effective network state classification is a primary task for ensuring network security and optimizing performance. Existing deep learning models have shown considerable progress in this area. Some methods excel at analyzing the complex…