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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
Abstract
We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.
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Cites
Orthogonal Polynomials for Engineers and Physicists
L., Y. L., & Beckmann, P. (1974) · Mathematics of Computation · doi:10.2307/2005720 · Cited by 169
Cited by
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Self-citationZhu, Y., & Zabaras, N. (2018) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.04.018 · Cited by 704
Simulation-based optimal bayesian experimental design for nonlinear systems
Huan, X., & Marzouk, Y. M. (2013) · Journal of Computational Physics · doi:10.1016/j.jcp.2012.08.013 · Cited by 438
“Many options exist, ranging from projection-based model reduction [45, 46] to spectral methods based on polynomial chaos (PC) expansions [47, 22, 23, 48, 49, 50, 51].”
BackgroundMethodMachine learning for high-dimensional dynamic stochastic economies
Scheidegger, S., & Bilionis, I. (2019) · Journal of Computational Science · doi:10.1016/j.jocs.2019.03.004 · Cited by 72
A Data-Driven Diagnostic Framework for Wind Turbine Structures: A Holistic Approach
Bogoevska, S., Spiridonakos, M., Chatzi, E., Dumova-Jovanoska, E., & Höffer, R. (2017) · Sensors · doi:10.3390/s17040720 · Cited by 60
Metadata
- Authors
- Xiu, D., & Karniadakis, G. E.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2002-01
- Volume
- 24
- Issue
- 2
- Pages
- 619-644
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2018159038
- Cited by
- 4,807
- References
- 1
- FWCI
- 35.34
- Type
- journal article
- Language
- en
- Open access
- closed
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