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This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…

High-dimensional datasets present substantial challenges in statistical modeling across various disciplines, necessitating effective dimensionality reduction methods. Deep learning approaches, notable for their capacity to distill essential…

Accurate surface estimation is critical for downstream tasks in scientific simulation, and quantifying uncertainty in implicit neural 3D representations still remains a substantial challenge due to computational inefficiencies, scalability…

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Large eddy simulation (LES) is an alternative that is computationally less demanding, but is…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…

Direct numerical simulations (DNS) are one of the main ab initio tools to study turbulent flows. However, due to their considerable computational cost, DNS are primarily restricted to canonical flows at moderate Reynolds numbers, in which…

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model…

Non-rigid registration is challenging because it is ill-posed with high degrees of freedom and is thus sensitive to noise and outliers. We propose a robust non-rigid registration method using reweighted sparsities on position and…

The high dimensionality of kinetic equations with stochastic parameters poses major computational challenges for uncertainty quantification (UQ). Traditional Monte Carlo (MC) sampling methods, while widely used, suffer from slow convergence…

Newtonian machine learning (NML) is a wave-equation inversion method that inverts single-dimensional latent space (LS) features of the seismic data for retrieving the subsurface background velocity model. The single-dimensional LS features…

Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…

Instabilities arise in a number of flow configurations. One such manifestation is the development of interfacial waves in multiphase flows, such as those observed in the falling liquid film problem. Controlling the development of such…

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

Transient computational fluid dynamics (CFD) remains expensive when long horizons and multi-scale turbulence are involved. Data-driven surrogates promise relief, yet many degrade over multiple steps or drift from physical behavior. This…

Sparse Representation (SR) techniques encode the test samples into a sparse linear combination of all training samples and then classify the test samples into the class with the minimum residual. The classification of SR techniques depends…