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1. Efficiency of Uncertainty Propagation Methods for Estimating Output Moments

   https://doi.org/10.1016/B978-0-12-818597-1.50078-3  

   Mohammadi, Samira ; Cremaschi, Selen ( July 2019 , Computeraided Chemical Engineering)

   Uncertainty propagation methods are used to estimate the distribution of model outputs resulting from a set of uncertain model outputs. There are a number of uncertainty propagation methods available in literature. This paper compares six non-intrusive uncertainty propagation methods, Latin Hypercube Sampling, Full Factorial Integration, Univariate Dimension Reduction, Halton series, Sobol series, and Polynomial Chaos Expansion, in terms of their efficiency for estimating the first four moments of the output distribution using computational experiments. The results suggest employing FFNI if there are few uncertain inputs, up to three. Uncertainty propagation methods that utilize Halton and Sobol series are found to be robust for estimating output moments as the number of uncertain inputs increased. In general, higher order polynomial chaos expansion approximations (3rd-5th order) obtained accurate estimates of model outputs with fewer model evaluations. 

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2. Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for vascular haemodynamics

   https://doi.org/10.1002/cnm.3836  

   Schäfer, Friederike ; Schiavazzi, Daniele_E ; Hellevik, Leif_Rune ; Sturdy, Jacob ( June 2024 , International Journal for Numerical Methods in Biomedical Engineering)

   Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample‐based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol’ sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three‐dimensional fluid–structure interaction simulations with affordable one‐ and zero‐dimensional reduced‐order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi‐ (1D/0D) and tri‐fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single‐fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol’ indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

    

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3. Global Sensitivity Analysis and Uncertainty Quantification for Background Solar Wind Using the Alfvén Wave Solar Atmosphere Model

   https://doi.org/10.1029/2022SW003262  

   Jivani, Aniket ; Sachdeva, Nishtha ; Huang, Zhenguang ; Chen, Yang ; van der Holst, Bart ; Manchester, Ward ; Iong, Daniel ; Chen, Hongfan ; Zou, Shasha ; Huan, Xun ; et al ( January 2023 , Space Weather)

   Modeling the impact of space weather events such as coronal mass ejections (CMEs) is crucial to protecting critical infrastructure. The Space Weather Modeling Framework is a state‐of‐the‐art framework that offers full Sun‐to‐Earth simulations by computing the background solar wind, CME propagation, and magnetospheric impact. However, reliable long‐term predictions of CME events require uncertainty quantification (UQ) and data assimilation. We take the first steps by performing global sensitivity analysis (GSA) and UQ for background solar wind simulations produced by the Alfvén Wave Solar atmosphere Model (AWSoM) for two Carrington rotations: CR2152 (solar maximum) and CR2208 (solar minimum). We conduct GSA by computing Sobol' indices that quantify contributions from model parameter uncertainty to the variance of solar wind speed and density at 1 au, both crucial quantities for CME propagation and strength. Sobol' indices also allow us to rank and retain only the most important parameters, which aids in the construction of smaller ensembles for the reduced‐dimension parameter space. We present an efficient procedure for computing the Sobol' indices using polynomial chaos expansion surrogates and space‐filling designs. The PCEs further enable inexpensive forward UQ. Overall, we identify three important model parameters: the multiplicative factor applied to the magnetogram, Poynting flux per magnetic field strength constant used at the inner boundary, and the coefficient of the perpendicular correlation length in the turbulent cascade model in AWSoM.

    

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4. Atomistic simulation assisted error-inclusive Bayesian machine learning for probabilistically unraveling the mechanical properties of solidified metals

   https://doi.org/10.1038/s41524-024-01200-1  

   Mahata, A. ; Mukhopadhyay, T. ; Chakraborty, S. ; Asle Zaeem, M. ( January 2024 , npj Computational Materials)

   Solidification phenomenon has been an integral part of the manufacturing processes of metals, where the quantification of stochastic variations and manufacturing uncertainties is critically important. Accurate molecular dynamics (MD) simulations of metal solidification and the resulting properties require excessive computational expenses for probabilistic stochastic analyses where thousands of random realizations are necessary. The adoption of inadequate model sizes and time scales in MD simulations leads to inaccuracies in each random realization, causing a large cumulative statistical error in the probabilistic results obtained through Monte Carlo (MC) simulations. In this work, we present a machine learning (ML) approach, as a data-driven surrogate to MD simulations, which only needs a few MD simulations. This efficient yet high-fidelity ML approach enables MC simulations for full-scale probabilistic characterization of solidified metal properties considering stochasticity in influencing factors like temperature and strain rate. Unlike conventional ML models, the proposed hybrid polynomial correlated function expansion here, being a Bayesian ML approach, is data efficient. Further, it can account for the effect of uncertainty in training data by exploiting mean and standard deviation of the MD simulations, which in principle addresses the issue of repeatability in stochastic simulations with low variance. Stochastic numerical results for solidified aluminum are presented here based on complete probabilistic uncertainty quantification of mechanical properties like Young’s modulus, yield strength and ultimate strength, illustrating that the proposed error-inclusive data-driven framework can reasonably predict the properties with a significant level of computational efficiency.

    

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5. Efficient Global Sensitivity Analysis of Model-Based Ultrasonic Nondestructive Testing Systems Using Machine Learning and Sobol’ Indices

   https://doi.org/10.1115/1.4051100  

   Nagawkar, Jethro ; Leifsson, Leifur ( November 2021 , Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems)

   null (Ed.)

   Abstract The objective of this work is to reduce the cost of performing model-based sensitivity analysis for ultrasonic nondestructive testing systems by replacing the accurate physics-based model with machine learning (ML) algorithms and quickly compute Sobol’ indices. The ML algorithms considered in this work are neural networks (NNs), convolutional NN (CNNs), and deep Gaussian processes (DGPs). The performance of these algorithms is measured by the root mean-squared error on a fixed number of testing points and by the number of high-fidelity samples required to reach a target accuracy. The algorithms are compared on three ultrasonic testing benchmark cases with three uncertainty parameters, namely, spherically void defect under a focused and a planar transducer and spherical-inclusion defect under a focused transducer. The results show that NNs required 35, 100, and 35 samples for the three cases, respectively. CNNs required 35, 100, and 56, respectively, while DGPs required 84, 84, and 56, respectively. 

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