Related papers: Gaussian Process Regression and Conditional Polyno…

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by…

This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of training data is…

Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on…

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…

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…

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually…

Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by…