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Optimized sparse polynomial chaos expansion with entropy regularization [PDF]
Advances in Aerodynamics, 2022 Sparse Polynomial Chaos Expansion (PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviating the problem of dimensionality curse.
Sijie Zeng +3 more
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Polynomial Chaos Expansion Approach to Interest Rate Models [PDF]
Journal of Probability and Statistics, 2015 The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity ξ, hence acting as a kind of ...
Luca Di Persio +2 more
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Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion [PDF]
Entropy, 2018 To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects.
Jianyu Zhao +3 more
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Bayesian Adaptive Polynomial Chaos Expansions
Stat, Volume 15, Issue 1, March 2026.Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare, especially with implementations in R.
Rumsey, Kellin N. +4 more
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Best Practices in Developing a Workflow for Uncertainty Quantification for Modeling the Biodegradation of Mg‐Based Implants [PDF]
Advanced ScienceComputational models of electrochemical biodegradation of magnesium (Mg)‐based implants are uncertain. To quantify the model uncertainty, iterative evaluations are needed.
Tamadur AlBaraghtheh +2 more
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Study on precision reliability evaluation method of harmonic drive based on NIPCE considering wear [PDF]
Scientific ReportsA dynamic reliability evaluation method for precision of harmonic drive considering wear is proposed to estimate the precision reliability of harmonic drive precisely for precision degradation failure prediction and proactive maintenance.
Xian Zhang +4 more
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HIERARCHICAL ADAPTIVE POLYNOMIAL CHAOS EXPANSIONS [PDF]
Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015), 2015 Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact ...
Mai, Chu V., Sudret, Bruno
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Mathematics, 2023 The evaluation of objective functions and component reliability in the optimisation of structural-acoustic systems with random and interval variables is computationally expensive, especially when strong nonlinearity exhibits between the response and ...
Shengwen Yin +3 more
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Physics-informed polynomial chaos expansions
Journal of Computational Physics, 2023 Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the known physics of the model.
Lukáš Novák +2 more
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Shock and Vibration, 2021 For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain ...
Shengwen Yin, Xiaohan Zhu, Xiang Liu
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