The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations. https://app.cochat.ai/papers/10.1137/s1064827501387826
- The paper
- Xiu, D., & Karniadakis, G. E. (2002). The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing. https://doi.org/10.1137/s1064827501387826
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
