Related papers: A Spline Chaos Expansion
We introduce here Cartesian splines or, for short, C-splines. C- splines are piecewise polynomials which are defined on adjacent Cartesian coordinate systems and are Cr continuous throughout. The Cr continuity is enforced by constraining…
Correlation and smoothness are terms used to describe a wide variety of random quantities. In time, space, and many other domains, they both imply the same idea: quantities that occur closer together are more similar than those further…
The requirement to generate robust robotic platforms is a critical enabling step to allow such platforms to permeate safety-critical applications (i.e., the localization of autonomous platforms in urban environments). One of the primary…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…
The cross-entropy (CE) method is a popular stochastic method for optimization due to its simplicity and effectiveness. Designed for rare-event simulations where the probability of a target event occurring is relatively small, the CE-method…
Large language models (LLMs) have demonstrated remarkable performance, yet their diverse strengths and weaknesses prevent any single LLM from achieving dominance across all tasks. Ensembling multiple LLMs is a promising approach to generate…
This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation…
Conformal Prediction (CP) is a distribution-free framework for constructing statistically rigorous prediction sets. While popular variants such as CD-split improve CP's efficiency, they often yield prediction sets composed of multiple…
Unmeasured, spatially-structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the…
In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…
Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However,…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We…
This study proposes median consensus embedding (MCE) to address variability in low-dimensional embeddings caused by random initialization in nonlinear dimensionality reduction techniques such as $t$-distributed stochastic neighbor…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…