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1. Optimization framework for patient‐specific modeling under uncertainty

   https://doi.org/10.1002/cnm.3665  

   Mineroff, Joshua; Pokuri, Balaji Sesha Sarath; Ganapathysubramanian, Baskar; Krishnamurthy, Adarsh (December 2022, International Journal for Numerical Methods in Biomedical Engineering)

   Abstract Estimating a patient‐specific computational model's parameters relies on data that is often unreliable and ill‐suited for a deterministic approach. We develop an optimization‐based uncertainty quantification framework for probabilistic model tuning that discovers model inputs distributions that generate target output distributions. Probabilistic sampling is performed using a surrogate model for computational efficiency, and a general distribution parameterization is used to describe each input. The approach is tested on seven patient‐specific modeling examples using CircAdapt, a cardiovascular circulatory model. Six examples are synthetic, aiming to match the output distributions generated using known reference input data distributions, while the seventh example uses real‐world patient data for the output distributions. Our results demonstrate the accurate reproduction of the target output distributions, with a correct recreation of the reference inputs for the six synthetic examples. Our proposed approach is suitable for determining the parameter distributions of patient‐specific models with uncertain data and can be used to gain insights into the sensitivity of the model parameters to the measured data. 

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2. Surrogate Model Selection for Design Space Approximation and Surrogate-based Optimization

   https://doi.org/10.1016/B978-0-12-818597-1.50056-4  

   Williams, Bianca; Cremaschi, Selen (July 2019, Computeraided Chemical Engineering)

   Surrogate models are used to map input data to output data when the actual relationship between the two is unknown or computationally expensive to evaluate for sensitivity analysis, uncertainty propagation and surrogate based optimization. This work evaluates the performance of eight surrogate modeling techniques for design space approximation and surrogate based optimization applications over a set of generated datasets with known characteristics. With this work, we aim to provide general rules for selecting an appropriate surrogate model form solely based on the characteristics of the data being modeled. The computational experiments revealed that, in general, multivariate adaptive regression spline models (MARS) and single hidden layer feed forward neural networks (ANN) yielded the most accurate predictions over the design space while Random Forest (RF) models most reliably identified the locations of the optimums when used for surrogate-based optimization. 

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3. Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

   https://doi.org/s10596-021-10085-8  

   Cleaves, Helen; Alexanderian, Alen; Saad, Bilal (December 2021, Computational geosciences)

   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-Loeve (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. 

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4. Surrogate modeling of structural seismic response using probabilistic learning on manifolds

   https://doi.org/10.1002/eqe.3839  

   Zhong, Kuanshi; Navarro, Javier G.; Govindjee, Sanjay; Deierlein, Gregory G. (February 2023, Earthquake Engineering & Structural Dynamics)

   Abstract Nonlinear response history analysis (NLRHA) is generally considered to be a reliable and robust method to assess the seismic performance of buildings under strong ground motions. While NLRHA is fairly straightforward to evaluate individual structures for a select set of ground motions at a specific building site, it becomes less practical for performing large numbers of analyses to evaluate either (1) multiple models of alternative design realizations with a site‐specific set of ground motions, or (2) individual archetype building models at multiple sites with multiple sets of ground motions. In this regard, surrogate models offer an alternative to running repeated NLRHAs for variable design realizations or ground motions. In this paper, a recently developed surrogate modeling technique, called probabilistic learning on manifolds (PLoM), is presented to estimate structural seismic response. Essentially, the PLoM method provides an efficient stochastic model to develop mappings between random variables, which can then be used to efficiently estimate the structural responses for systems with variations in design/modeling parameters or ground motion characteristics. The PLoM algorithm is introduced and then used in two case studies of 12‐story buildings for estimating probability distributions of structural responses. The first example focuses on the mapping between variable design parameters of a multidegree‐of‐freedom analysis model and its peak story drift and acceleration responses. The second example applies the PLoM technique to estimate structural responses for variations in site‐specific ground motion characteristics. In both examples, training data sets are generated for orthogonal input parameter grids, and test data sets are developed for input parameters with prescribed statistical distributions. Validation studies are performed to examine the accuracy and efficiency of the PLoM models. Overall, both examples show good agreement between the PLoM model estimates and verification data sets. Moreover, in contrast to other common surrogate modeling techniques, the PLoM model is able to preserve correlation structure between peak responses. Parametric studies are conducted to understand the influence of different PLoM tuning parameters on its prediction accuracy. 

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5. Iterative Global Sensitivity Analysis Algorithm with Neural Network Surrogate Modeling

   https://doi.org/10.1007/978-3-030-77970-2_23  

   Liu, Y.C.; Nagawkar, J.; Leifsson, L.; Koziel, S.; Pietrenko-Dabrowska, A. (June 2021, Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science)

   Paszynski, M.; Kranzlmüller, D.; Krzhizhanovskaya, V.V.; Dongarra, J.J.; Sloot, P.M. (Ed.)

   Global sensitivity analysis (GSA) is a method to quantify the effect of the input parameters on outputs of physics-based systems. Performing GSA can be challenging due to the combined effect of the high computational cost of each individual physics-based model, a large number of input parameters, and the need to perform repetitive model evaluations. To reduce this cost, neural networks (NNs) are used to replace the expensive physics-based model in this work. This introduces the additional challenge of finding the minimum number of training data samples required to train the NNs accurately. In this work, a new method is introduced to accurately quantify the GSA values by iterating over both the number of samples required to train the NNs, terminated using an outer-loop sensitivity convergence criteria, and the number of model responses required to calculate the GSA, terminated with an inner-loop sensitivity convergence criteria. The iterative surrogate-based GSA guarantees converged values for the Sobol’ indices and, at the same time, alleviates the specification of arbitrary accuracy metrics for the surrogate model. The proposed method is demonstrated in two cases, namely, an eight-variable borehole function and a three-variable nondestructive testing (NDT) case. For the borehole function, both the first- and total-order Sobol’ indices required 200 and 105 data points to terminate on the outer- and inner-loop sensitivity convergence criteria, respectively. For the NDT case, these values were 100 for both first- and total-order indices for the outer-loop sensitivity convergence, and 106 and 103 for the inner-loop sensitivity convergence, respectively, for the first- and total-order indices, on the inner-loop sensitivity convergence. The differences of the proposed method with GSA on the true functions are less than 3% in the analytical case and less than 10% in the physics-based case (where the large error comes from small Sobol’ indices). 

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