Uncertainty Quantification in CO2Sequestration Using Surrogate Models from Polynomial Chaos Expansion

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Surrogate model based uncertainty quantification of CFD simulations of the viscous flow around a ship advancing in shallow water

We propose a set of equations for preliminary risk‐targeted seismic design of structures base‐isolated using single friction pendulum (SFP) bearings. The equations offer statistical estimates of the maximum displacement of the superstructure relative to the base and the maximum displacement of the isolated base response quantities of interest (RQIs), given ground motion intensity measures and the essential dynamic properties of the SFP bearing base‐isolated structure. The set of proposed equations enables preliminary seismic design of SFP base‐isolated structures using the mean annual frequency of exceeding displacement‐defined limit states related to the two RQIs. To develop the design equations, we define and use a two‐degree‐of‐freedom (2DOF) surrogate model that features a few essential dynamic parameters of the SFP bearing base‐isolated structure. We first verify that the 2DOF surrogate model is accurate enough to represent the base and superstructure displacements compared to the complete multiple‐degree‐of‐freedom model of the prototype SFP bearing base‐isolated structure. Next, we perform more than 5 million non‐linear dynamical analyses of 4900 distinct 2DOF surrogates subjected to 210 different recorded ground motions scaled five times. We fit the response data of each 2DOF surrogate to a linear model and use two different modeling techniques to derive the design equations. One model is based on Polynomial Chaos Expansion (PCE), and the other model is based on Linear Regression (LR). The PCE model is more accurate than the LR model, with the trade‐off regarding its simplicity. Nevertheless, both the PCE and the LR models are accurate enough to estimate the design quantities of interest of the SFP bearing base‐isolated structure for preliminary design purposes. Lastly, we exemplify the use of the proposed design equations and we show that the estimate of base displacement is conservative in the cases when the superstructure of the SPF bearing base‐isolated structure yields.

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross-polarization of an inset-fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high-volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem-specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte-Carlo analysis.

Development of clustered polynomial chaos expansion model for stochastic hydrological prediction

Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation

The development of high-performance MEMS devices necessitates efficient design optimization and yield analysis in the presence of unavoidable process variations. The existing algorithms are not able to integrate the different requirements of optimization and uncertainty quantification (UQ), highlighting the necessity for a comprehensive algorithmic framework. To this end, a novel algorithm framework is proposed for the optimization and UQ of MEMS devices. The deep neural network (DNN) and polynomial chaos expansion (PCE) are respectively leveraged to build the global surrogate model for the nondominated sorting genetic algorithm II (NSGA-II) and the local surrogate model for the UQ analysis. The DNN is refined by the bi-fidelity data training scheme to reduce the training data demanded, and the active subspace dimension reduction (AS) is employed to fully utilize the information within the global surrogate model, thereby minimizing the computational resources needed for the local surrogate model construction. This algorithm is applied to a kind of MEMS thermal flow sensor. The proposed algorithmic simultaneously increases sensor sensitivity by 14.77% while reducing computational expenditure by 44.4% during the optimization phase. Besides, the yield analysis is also derived accurately, with computational cost reductions of 73.0%. These results indicate that this novel algorithm supplies an effective, accurate, and efficient technique for the optimization and yield analysis for MEMS devices. [2025-0231]

Performing uncertainty quantification (UQ) and sensitivity analysis (SA) is vital when developing a patient-specific physiological model because it can quantify model output uncertainty and estimate the effect of each of the model's input parameters on the mathematical model. By providing this information, UQ and SA act as diagnostic tools to evaluate model fidelity and compare model characteristics with expert knowledge and real world observation. Computational efficiency is an important part of UQ and SA methods and thus optimization is an active area of research. In this work, we investigate a new efficient sampling method for least-squares polynomial approximation, weighted approximate Fekete points (WAFP). We analyze the performance of this method by demonstrating its utility in stochastic analysis of a cardiovascular model that estimates changes in oxyhemoglobin saturation response. Polynomial chaos (PC) expansion using WAFP produced results similar to the more standard Monte Carlo in quantifying uncertainty and identifying the most influential model inputs (including input interactions) when modeling oxyhemoglobin saturation, PC expansion using WAFP was far more efficient. These findings show the usefulness of using WAFP based PC expansion to quantify uncertainty and analyze sensitivity of a oxyhemoglobin dissociation response model. Applying these techniques could help analyze the fidelity of other relevant models in preparation for clinical application.

Polynomial Chaos Expansion (PCE) Based Surrogate Modeling and Optimization for Batch Crystallization Processes

Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-valued outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loéve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.

Collision probability calculation is critical to space situational awareness or space traffic management. To determine the collision probability, the conjunction time needs to be determined first, but both collision probability and conjunction time usually exist large uncertainties. In this paper, a continuous representation of the polynomial chaos expansion (PCE)-based surrogate model is used to describe the uncertainty of space objects along with time. This PCE model facilitates the propagation of sampling points representing orbital uncertainty at any time. A machine learning-based Bayesian optimization method is employed to determine the conjunction time and then the collision probability. A data-driven Gaussian process regression model is built to approximate the Hausdorff distance, which is a distance metric between two space objects with uncertainty and is used as an objective function for Bayesian optimization. The proposed PCE model and Bayesian optimization do not require the Gaussian assumption and provide a general framework to calculate the conjunction time and collision probability. Two numerical experiments are used to show the effectiveness of the proposed algorithm and its close performance to the traditional Monte Carlo sampling-based method.

Renewable-powered ammonia production is a promising route for sustainable energy and hydrogen storage but is highly sensitive to operational uncertainty from variable power supply and component performance. This study presents a novel machine learning–enhanced uncertainty quantification (ML-UQ) framework that, for the first time, integrates a high-fidelity surrogate model—an artificial neural network with autoregressive feedback—into Aspen Plus simulations of a hybrid ammonia production system coupled with a vapour absorption refrigeration unit for heat recovery. The framework captures nonlinear interactions among six critical uncertain parameters, including renewable power variability, heat exchanger effectiveness, and compressor efficiency. It reduces the computational cost by three orders of magnitude while maintaining high predictive accuracy (R2 = 0.97, MAE = 8.57, RMSE = 11.3). The ANN surrogate enables scalable uncertainty propagation via polynomial chaos expansion. Results show that, across nominal power levels of 10–20 MW, uncertainties can cause up to 18 % variation in ammonia output, 30 % in refrigeration, and 40–50 % in CO2 emissions reduction. Heat exchanger effectiveness alone accounts for nearly 50 % of total variability. Economic analysis indicates a 5 % increase in the levelized cost of ammonia and 30–40 % variation in annual refrigeration revenue. This work delivers the first computationally feasible, ML-assisted surrogate-based UQ framework for hybrid green ammonia systems. More broadly, it offers a practical and readily scalable tool for designing resilient, economically viable, and low-carbon energy and chemical manufacturing systems.

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

Rapid design centering of multi-band antennas using knowledge-based inverse models and response features