About
Mathematical models are widely used in physics and engineering applications as predictive tools. However, in many situations, the input parameters of the model are uncertain due to either a lack of knowledge or an intrinsic variability of the system. Examples are the study of subsurface phenomena, biological tissues, complex materials, whose properties are often heterogeneous, not perfectly characterized and, possibly, changing in time in an uncertain way.
In this line of research we consider the case in which the uncertainty can be described reasonably well in a probabilistic setting and we focus on the problem of effectively propagating it from the input parameters to the output quantities of interest of the mathematical model. In particular we focus on non-intrusive numerical methods that imply solving the problem for a well chosen set of input parameters and make inference on the statistical properties of the output quantities based on the corresponding evaluations.
Publications
- Motamed, M., Nobile, F., & Tempone, R. (2012). A stochastic collocation method for the second order wave equation with a discontinuous random speed. Numerische Mathematik, 123(3), 493–536. doi:10.1007/s00211-012-0493-5 Handle 10754/562285
- BECK, J., TEMPONE, R., NOBILE, F., & TAMELLINI, L. (2012). ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS. Mathematical Models and Methods in Applied Sciences, 22(09), 1250023. doi:10.1142/s0218202512500236 Handle 10754/562295
- Long, Q., Scavino, M., Tempone, R., & Wang, S. (2013). Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations. Computer Methods in Applied Mechanics and Engineering, 259, 24–39. doi:10.1016/j.cma.2013.02.017 Handle 10754/562783
- Bäck, J., Nobile, F., Tamellini, L., & Tempone, R. (2010). Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison. Spectral and High Order Methods for Partial Differential Equations, 43–62. doi:10.1007/978-3-642-15337-2_3 Handle 10754/575778
- Babuška, I., Nobile, F., & Tempone, R. (2010). A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data. SIAM Review, 52(2), 317–355. doi:10.1137/100786356 Handle 10754/555664
Collaborators
- Raul F. Tempone, Professor, Applied Mathematics and Computational Sciences.