Related papers: Adaptive Density Tracking by Quadrature for Stocha…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…
This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a…
We propose the novel numerical scheme for solution of the multidimensional Fokker-Planck equation, which is based on the Chebyshev interpolation and the spectral differentiation techniques as well as low rank tensor approximations, namely,…
Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…
In this article we show in details the derivation of an integration scheme for the dissipative particle dynamic model (DPD) using the stochastic Trotter formula [De Fabritiis et al., Physica A, 361, 429 (2006)]. We explain some subtleties…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the…
Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…
We establish a continuous-time framework for analyzing Deep Q-Networks (DQNs) via stochastic control and Forward-Backward Stochastic Differential Equations (FBSDEs). Considering a continuous-time Markov Decision Process (MDP) driven by a…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…
Trajectory clustering enables the discovery of common patterns in trajectory data. Current methods of trajectory clustering rely on a distance measure between two points in order to measure the dissimilarity between two trajectories. The…
Unsupervised learning of time series data, also known as temporal clustering, is a challenging problem in machine learning. Here we propose a novel algorithm, Deep Temporal Clustering (DTC), to naturally integrate dimensionality reduction…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…
Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming…
We derive the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatial coordinates,…
Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics, combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle…