相关论文: Active subspace methods in theory and practice: ap…

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Discrete response of structures is often a key probabilistic quantity of interest. For example, one may need to identify the probability of a binary event, such as, whether a structure has buckled or not. In this study, an adaptive…

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not…

We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…

This paper proposes a robust, high-precision positioning methodology to address localization failures arising from complex background interference in large-scale flight navigation and the computational inefficiency inherent in conventional…

Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an…

In this paper we develop an adaptive transform-domain technique based on rational function systems. It is of general importance in several areas of signal theory, including filter design, transfer function approximation, system…

Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may…

The product design process in manufacturing involves iterative design modeling and analysis to achieve the target engineering performance, but such an iterative process is time consuming and computationally expensive. Recently, deep…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

In this paper we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the method proposed in our previous…

In recent years, genetic programming (GP)-based evolutionary feature construction has achieved significant success. However, a primary challenge with evolutionary feature construction is its tendency to overfit the training data, resulting…

Construction of kinetic models has become an indispensable step in the development and scale up of processes in the industry. Model-based design of experiments (MBDoE) has been widely used for the purpose of improving parameter precision in…

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical…