- -

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

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • 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

Mostrar el registro completo del ítem

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

Ficheros en el ítem

Metadatos del ítem

Título: Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models
Autor: Calatayud-Gregori, Julia Chen-Charpentier, Benito M. Cortés, J.C. Jornet-Sanz, Marc
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[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 ...[+]
Palabras clave: Uncertainty quantification , Epidemiological stochastic model , Probability density function , Generalized polynomial chaos , Random variable transformation technique
Derechos de uso: Reconocimiento (by)
Fuente:
Symmetry (Basel). (eissn: 2073-8994 )
DOI: 10.3390/sym11010043
Editorial:
MDPI AG
Versión del editor: https://doi.org/10.3390/sym11010043
Código del Proyecto:
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/
Agradecimientos:
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 ...[+]
Tipo: 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

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem