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

Systematic exploration of Agent-Based Models (ABMs) is challenged by the curse of dimensionality and their inherent stochasticity. We present a multi-stage pipeline integrating the systematic design of experiments with machine learning…

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…

Determining the proper level of details to develop and solve physical models is usually difficult when one encounters new engineering problems. Such difficulty comes from how to balance the time (simulation cost) and accuracy for the…

This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…

This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the…

Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…

Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using…

Stochastic simulation has been widely used to analyze the performance of complex stochastic systems and facilitate decision making in those systems. Stochastic simulation is driven by the input model, which is a collection of probability…

Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the…

Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Bayesian Optimization is a popular approach for optimizing expensive black-box functions. Its key idea is to use a surrogate model to approximate the objective and, importantly, quantify the associated uncertainty that allows a sequential…

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Multifidelity surrogate modelling combines data of varying accuracy and cost from different sources. It strategically uses low-fidelity models for rapid evaluations, saving computational resources, and high-fidelity models for detailed…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance…

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…