Related papers: Bounded KRnet and its applications to density esti…

A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic H\"{o}rmander condition, and empirically in numerical examples. In a prediction…

Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from…

We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…

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…

BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically…

Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…

A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…

In recent years, using a deep convolutional neural network (CNN) as a feature encoder (or backbone) is the most commonly observed architectural pattern in several computer vision methods, and semantic segmentation is no exception. The two…

Deep neural networks face several challenges in hyperspectral image classification, including high-dimensional data, sparse distribution of ground objects, and spectral redundancy, which often lead to classification overfitting and limited…

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,…

The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a…

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),…

Kernel learning forward backward SDE filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real\-world graphs poorly by fixed\-curvature space due to…

Stochastic differential equations are commonly used to describe the evolution of stochastic processes. The state uncertainty of such processes is best represented by the probability density function (PDF), whose evolution is governed by the…

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…

Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full precision counterparts. To maintain the same performance level especially at low bit-widths,…