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1. Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems

   https://doi.org/10.3390/applmech1030011  

   Son, Jeongeun ; Du, Dongping ; Du, Yuncheng ( September 2020 , Applied Mechanics)

   null (Ed.)

   Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive because it often involves high-dimensional integrals. To address this, a generalized dimension reduction method (gDRM) is coupled with quadrature rules to convert a high-dimensional integral in the SG into a few lower dimensional ones that can be rapidly solved. The performance of the algorithm is validated with two examples describing the dynamic behavior of cells. Compared to other UQ techniques (e.g., nonintrusive PCE), the results show the potential of the algorithm to tackle UQ in more complicated biological systems. 

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2. 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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3. Quantification and propagation of Aleatoric uncertainties in topological structures

   https://doi.org/10.1016/j.ress.2023.109122  

   Wang, Zihan ; Daeipour, Mohamad ; Xu, Hongyi ( May 2023 , Reliability Engineering & System Safety)

   Quantification and propagation of aleatoric uncertainties distributed in complex topological structures remain a challenge. Existing uncertainty quantification and propagation approaches can only handle parametric uncertainties or high dimensional random quantities distributed in a simply connected spatial domain. There lacks a systematic method that captures the topological characteristics of the structural domain in uncertainty analysis. Therefore, this paper presents a new methodology that quantifies and propagates aleatoric uncertainties, such as the spatially varying local material properties and defects, distributed in a topological spatial domain. We propose a new random field-based uncertainty representation approach that captures the topological characteristics using the shortest interior path distance. Parameterization methods like PPCA and β-Variational Autoencoder (βVAE) are employed to convert the random field representation of uncertainty to a small set of independent random variables. Then non-intrusive uncertainties propagation methods such as polynomial chaos expansion and univariate dimension reduction are employed to propagate the parametric uncertainties to the output of the problem. The effectiveness of the proposed methodology is demonstrated by engineering case studies. The accuracy and computational efficiency of the proposed method is confirmed by comparing with the reference values of Monte Carlo simulations with a sufficiently large number of samples. 

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4. Representing model uncertainties in brittle fracture simulations

   https://doi.org/10.1016/j.cma.2023.116575  

   Zhang, Hao ; Dolbow, John E. ; Guilleminot, Johann ( January 2024 , Computer Methods in Applied Mechanics and Engineering)

   This work focuses on the representation of model-form uncertainties in phase-field models of brittle fracture. Such uncertainties can arise from the choice of the degradation function for instance, and their consideration has been unaddressed to date. The stochastic modeling framework leverages recent developments related to the analysis of nonlinear dynamical systems and relies on the construction of a stochastic reduced-order model. In the latter, a POD-based reduced-order basis is randomized using Riemannian projection and retraction operators, as well as an information-theoretic formulation enabling proper concentration in the convex hull defined by a set of model proposals. The model thus obtained is mathematically admissible in the almost sure sense and involves a low-dimensional hyperparameter, the calibration of which is facilitated through the formulation of a quadratic programming problem. The relevance of the modeling approach is further assessed on one- and two-dimensional applications. It is shown that model uncertainties can be efficiently captured and propagated to macroscopic quantities of interest. An extension based on localized randomization is also proposed to handle the case where the forward simulation is highly sensitive to sample localization. This work constitutes a methodological development allowing phase-field predictions to be endowed with statistical measures of confidence, accounting for the variability induced by modeling choices. 

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5. Clustering Embedded Approaches for Efficient Information Network Inference

   https://doi.org/10.1007/s41019-015-0003-8  

   Hu, Qingbo ; Xie, Sihong ; Lin, Shuyang ; Wang, Senzhang ; Yu, Philip S. ( September 2015 , Data Science and Engineering)

   Nowadays, the message diffusion links among users or Web sites drive the development of countless innovative applications. However, in reality, it is easier for us to observe the time stamps when different nodes in the network react on a message, while the connections empowering the diffusion of the message remain hidden. This motivates recent extensive studies on thenetwork inference problem: unveiling the edges from the records of messages disseminated through them. Existing solutions are computationally expensive, which motivates us to develop an efficient two-step general framework,Clustering Embedded Network Inference(CENI). CENI integrates clustering strategies to improve the efficiency of network inference. By clustering nodes directly on the time lines of messages, we propose two naive implementations of CENI:Infection-centric CENIandCascade-centric CENI. Additionally, we point out thecritical dimensionproblem of CENI: Instead of one-dimensional time lines, we need to first project the nodes to an Euclidean space of certain dimension before clustering. A CENI adopting clustering method on the projected space can better preserve the structure hidden in the cascades and generate more accurately inferred links. By addressing the critical dimension problem, we propose the third implementation of the CENI framework:Projection-based CENI. Through extensive experiments on two real datasets, we show that the three CENI models only need around 20–50 % of the running time of state-of-the-art methods. Moreover, the inferred edges of Projection-based CENI preserve or even outperform the effectiveness of state-of-the-art methods.

    

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