A Posteriori Validation of Generalized Polynomial Chaos Expansions
SIAM Journal on Applied Dynamical Systems, 2023 Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invariant sets associated to such equations. In this work, we use ideas from validated numerics in order to obtain rigorous a posteriori error estimates together with existence ...
Maxime Breden
openalex +5 more sources
A Generalized Polynomial Chaos-Based Approach to Analyze the Impacts of Process Deviations on MEMS Beams [PDF]
Sensors, 2017 A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc.
Lili Gao, Zai-Fa Zhou, Qing-An Huang
doaj +2 more sources
Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification
Journal of Computational Physics, 2023 We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the gradient (or sensitivity) of the Quantity of Interest with respect to the stochastic variables. This sensitivity is
Kyriakos D. Kantarakias +1 more
openalex +4 more sources
Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach [PDF]
SIAM Journal on Scientific Computing, 2019 We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs. Given a stochastic input with an arbitrary probability measure, its random space is decomposed into smaller elements.
Cherif Snoun +2 more
openalex +3 more sources
Inverse Modeling of Hydrologic Parameters in CLM4 via Generalized Polynomial Chaos in the Bayesian Framework [PDF]
Computation, 2022 In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great ...
Georgios Karagiannis +3 more
doaj +2 more sources
A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS [PDF]
International Journal for Uncertainty Quantification, 2019 Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion.
Xiu Yang +3 more
openalex +4 more sources
Probabilistic load flow by generalized polynomial chaos method
2016 IEEE Power and Energy Society General Meeting (PESGM), 2016 The probabilistic load flow (PLF) problem is solved by a new approach named generalized polynomial chaos (gPC) method. This method combines the techniques of gPC expansion and Galerkin method and transforms the PLF equations into a set of deterministic equations.
Hao Wu +4 more
openalex +3 more sources
Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling [PDF]
Algorithms, 2020 Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest.
Claudia Zoccarato +3 more
doaj +2 more sources
, 2016 The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for high-dimensional input parameters is that the size of many parametric sampling meshes grows exponentially in the number of ...
Jiahua Jiang, Yanlai Chen, Akil Narayan
openalex +4 more sources
Generalized Decoupled Polynomial Chaos for Nonlinear Circuits With Many Random Parameters [PDF]
IEEE Microwave and Wireless Components Letters, 2015 This letter proposes a general and effective decoupled technique for the stochastic simulation of nonlinear circuits via polynomial chaos. According to the standard framework, stochastic circuit waveforms are still expressed as expansions of orthonormal polynomials.
Paolo Manfredi +3 more
openalex +5 more sources