Related papers: Dimensionality reduction can be used as a surrogat…

High-fidelity models are essential for accurately capturing nonlinear system dynamics. However, simulation of these models is often computationally too expensive and, due to their complexity, they are not directly suitable for analysis,…

We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…

We tackle the problem of quantifying failure probabilities for expensive deterministic computer experiments with stochastic inputs under a fixed budget. The computational cost of the computer simulation prohibits direct Monte Carlo (MC) and…

We introduce the concept of decision-focused surrogate modeling for solving computationally challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex,…

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…

The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future,…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…

Surrogate models are used to reduce the burden of expensive-to-evaluate objective functions in optimization. By creating models which map genomes to objective values, these models can estimate the performance of unknown inputs, and so be…

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for…

Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variations, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis…

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and…