- -

Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

  • Estadisticas de Uso

Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

Show full item record

Calatayud-Gregori, J.; Chen-Charpentier, BM.; Cortés, J.; Jornet-Sanz, M. (2019). Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models. Symmetry (Basel). 11(1):1-28. https://doi.org/10.3390/sym11010043

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/140420

Files in this item

Item Metadata

Title: Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models
Author: Calatayud-Gregori, Julia Chen-Charpentier, Benito M. Cortés, J.C. Jornet-Sanz, Marc
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions ...[+]
Subjects: Uncertainty quantification , Epidemiological stochastic model , Probability density function , Generalized polynomial chaos , Random variable transformation technique
Copyrigths: Reconocimiento (by)
Source:
Symmetry (Basel). (eissn: 2073-8994 )
DOI: 10.3390/sym11010043
Publisher:
MDPI AG
Publisher version: https://doi.org/10.3390/sym11010043
Project ID:
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/
Thanks:
This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y ...[+]
Type: Artículo

References

Strand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2

Bharucha-Reid, A. T. (1964). On the theory of random equations. Proceedings of Symposia in Applied Mathematics, 40-69. doi:10.1090/psapm/016/0189071

Xiu, D., & Karniadakis, G. E. (2002). The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24(2), 619-644. doi:10.1137/s1064827501387826 [+]
Strand, J. . (1970). Random ordinary differential equations. Journal of Differential Equations, 7(3), 538-553. doi:10.1016/0022-0396(70)90100-2

Bharucha-Reid, A. T. (1964). On the theory of random equations. Proceedings of Symposia in Applied Mathematics, 40-69. doi:10.1090/psapm/016/0189071

Xiu, D., & Karniadakis, G. E. (2002). The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24(2), 619-644. doi:10.1137/s1064827501387826

Chen-Charpentier, B.-M., Cortés, J.-C., Licea, J.-A., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., & Villanueva, R.-J. (2015). Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach. Mathematics and Computers in Simulation, 109, 113-129. doi:10.1016/j.matcom.2014.09.002

Cortés, J.-C., Romero, J.-V., Roselló, M.-D., & Villanueva, R.-J. (2017). Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique. Communications in Nonlinear Science and Numerical Simulation, 50, 1-15. doi:10.1016/j.cnsns.2017.02.011

Chen-Charpentier, B. M., & Stanescu, D. (2010). Epidemic models with random coefficients. Mathematical and Computer Modelling, 52(7-8), 1004-1010. doi:10.1016/j.mcm.2010.01.014

Lucor, D., Su, C.-H., & Karniadakis, G. E. (2004). Generalized polynomial chaos and random oscillators. International Journal for Numerical Methods in Engineering, 60(3), 571-596. doi:10.1002/nme.976

Santonja, F., & Chen-Charpentier, B. (2012). Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos. Computational and Mathematical Methods in Medicine, 2012, 1-8. doi:10.1155/2012/742086

Stanescu, D., & Chen-Charpentier, B. M. (2009). Random coefficient differential equation models for bacterial growth. Mathematical and Computer Modelling, 50(5-6), 885-895. doi:10.1016/j.mcm.2009.05.017

Calatayud, J., Cortés, J. C., Jornet, M., & Villanueva, R. J. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences, 41(18), 9618-9627. doi:10.1002/mma.5315

Villegas, M., Augustin, F., Gilg, A., Hmaidi, A., & Wever, U. (2012). Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties. Mathematics and Computers in Simulation, 82(5), 805-817. doi:10.1016/j.matcom.2011.12.001

Xiu, D., & Em Karniadakis, G. (2002). Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Computer Methods in Applied Mechanics and Engineering, 191(43), 4927-4948. doi:10.1016/s0045-7825(02)00421-8

Shi, W., & Zhang, C. (2012). Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations. Applied Numerical Mathematics, 62(12), 1954-1964. doi:10.1016/j.apnum.2012.08.007

Calatayud, J., Cortés, J.-C., & Jornet, M. (2018). On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations. Journal of Nonlinear Sciences and Applications, 11(09), 1077-1084. doi:10.22436/jnsa.011.09.06

Casabán, M.-C., Cortés, J.-C., Romero, J.-V., & Roselló, M.-D. (2015). Probabilistic solution of random SI-type epidemiological models using the Random Variable Transformation technique. Communications in Nonlinear Science and Numerical Simulation, 24(1-3), 86-97. doi:10.1016/j.cnsns.2014.12.016

Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009

Dorini, F. A., & Cunha, M. C. C. (2008). Statistical moments of the random linear transport equation. Journal of Computational Physics, 227(19), 8541-8550. doi:10.1016/j.jcp.2008.06.002

Hussein, A., & Selim, M. M. (2012). Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Applied Mathematics and Computation, 218(13), 7193-7203. doi:10.1016/j.amc.2011.12.088

Hussein, A., & Selim, M. M. (2015). Solution of the stochastic generalized shallow-water wave equation using RVT technique. The European Physical Journal Plus, 130(12). doi:10.1140/epjp/i2015-15249-3

Hussein, A., & Selim, M. M. (2013). A general analytical solution for the stochastic Milne problem using Karhunen–Loeve (K–L) expansion. Journal of Quantitative Spectroscopy and Radiative Transfer, 125, 84-92. doi:10.1016/j.jqsrt.2013.03.018

Xu, Z., Tipireddy, R., & Lin, G. (2016). Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Applied Mathematical Modelling, 40(9-10), 5542-5559. doi:10.1016/j.apm.2015.12.041

Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2017). Full solution of random autonomous first-order linear systems of difference equations. Application to construct random phase portrait for planar systems. Applied Mathematics Letters, 68, 150-156. doi:10.1016/j.aml.2016.12.015

El-Tawil, M. A. (2005). The approximate solutions of some stochastic differential equations using transformations. Applied Mathematics and Computation, 164(1), 167-178. doi:10.1016/j.amc.2004.04.062

Calatayud, J., Cortés, J.-C., & Jornet, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function. Physica A: Statistical Mechanics and its Applications, 512, 261-279. doi:10.1016/j.physa.2018.08.024

Calatayud, J., Cortés, J. C., & Jornet, M. (2018). Uncertainty quantification for random parabolic equations with nonhomogeneous boundary conditions on a bounded domain via the approximation of the probability density function. Mathematical Methods in the Applied Sciences, 42(17), 5649-5667. doi:10.1002/mma.5333

Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function. Applied Mathematics and Computation, 331, 33-45. doi:10.1016/j.amc.2018.02.051

Casabán, M.-C., Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Villanueva, R.-J. (2016). A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Communications in Nonlinear Science and Numerical Simulation, 32, 199-210. doi:10.1016/j.cnsns.2015.08.009

Kegan, B., & West, R. W. (2005). Modeling the simple epidemic with deterministic differential equations and random initial conditions. Mathematical Biosciences, 194(2), 217-231. doi:10.1016/j.mbs.2005.02.002

Crestaux, T., Le Maıˆtre, O., & Martinez, J.-M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety, 94(7), 1161-1172. doi:10.1016/j.ress.2008.10.008

Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93(7), 964-979. doi:10.1016/j.ress.2007.04.002

Chen-Charpentier, B. M., Cortés, J.-C., Romero, J.-V., & Roselló, M.-D. (2013). Some recommendations for applying gPC (generalized polynomial chaos) to modeling: An analysis through the Airy random differential equation. Applied Mathematics and Computation, 219(9), 4208-4218. doi:10.1016/j.amc.2012.11.007

Ernst, O. G., Mugler, A., Starkloff, H.-J., & Ullmann, E. (2011). On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 317-339. doi:10.1051/m2an/2011045

Giraud, L., Langou, J., & Rozloznik, M. (2005). The loss of orthogonality in the Gram-Schmidt orthogonalization process. Computers & Mathematics with Applications, 50(7), 1069-1075. doi:10.1016/j.camwa.2005.08.009

Marzouk, Y. M., Najm, H. N., & Rahn, L. A. (2007). Stochastic spectral methods for efficient Bayesian solution of inverse problems. Journal of Computational Physics, 224(2), 560-586. doi:10.1016/j.jcp.2006.10.010

Marzouk, Y., & Xiu, D. (2009). A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems. Communications in Computational Physics, 6(4), 826-847. doi:10.4208/cicp.2009.v6.p826

SCOTT, D. W. (1979). On optimal and data-based histograms. Biometrika, 66(3), 605-610. doi:10.1093/biomet/66.3.605

National Spanish Health Survey (Encuesta Nacional de Salud de España, ENSE)http://pestadistico.inteligenciadegestion.msssi.es/publicoSNS/comun/ArbolNodos.aspx

[-]

recommendations

 

This item appears in the following Collection(s)

Show full item record