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1. 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)

   Abstract 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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2. GLOBAL SENSITIVITY ANALYSIS MEASURES BASED ON STATISTICAL DISTANCES

   https://doi.org/10.1615/Int.J.UncertaintyQuantification.2021035424  

   Nandi, Souransu; Singh, Tarunraj (October 2021, International Journal for Uncertainty Quantification)

   null (Ed.)

   Global sensitivity analysis aims at quantifying and ranking the relative contribution of all the uncertain inputs of a mathematical model that impact the uncertainty in the output of that model, for any input-output mapping. Motivated by the limitations of the well-established Sobol' indices which are variance-based, there has been an interest in the development of non-moment-based global sensitivity metrics. This paper presents two complementary classes of metrics (one of which is a generalization of an already existing metric in the literature) which are based on the statistical distances between probability distributions rather than statistical moments. To alleviate the large computational cost associated with Monte Carlo sampling of the input-output model to estimate probability distributions, polynomial chaos surrogate models are proposed to be used. The surrogate models in conjunction with sparse quadrature-based rules, such as conjugate unscented transforms, permit efficient calculation of the proposed global sensitivity measures. Three benchmark sensitivity analysis examples are used to illustrate the proposed approach. 

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3. Response properties in phaseless auxiliary field quantum Monte Carlo

   https://doi.org/10.1063/5.0171996  

   Mahajan, Ankit; Kurian, Jo S.; Lee, Joonho; Reichman, David R.; Sharma, Sandeep (November 2023, The Journal of Chemical Physics)

   Unknown (Ed.)

   We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently. 

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4. Uncertainty quantification in stochastic economic dispatch using Gaussian process emulation

   Hu, Zhixiong; Xu, Yijun; Korkali, Mert; Chen, Xiao; Mili, Lamine; Tong, Charles H. (February 2020, IEEE ISGT NA 2020: "Enabling Intelligent and Resilient Communities")

   The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To solve this stochastic economic dispatch, the conventional Monte Carlo method is prohibitively time con- suming for medium- and large-scale power systems. To overcome this problem, we propose in this paper a novel Gaussian- process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Based on the dimension-reduction results obtained by the Karhunen-Loe`ve expansion, a Gaussian-process emulator is constructed. This surrogate allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus system reveal that the proposed method has an excellent performance as compared to the traditional Monte Carlo method. 

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5. Quantification of electron correlation for approximate quantum calculations

   https://doi.org/10.1063/5.0119260  

   Yuan, Shunyue; Chang, Yueqing; Wagner, Lucas K. (November 2022, The Journal of Chemical Physics)

   State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions. 

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