3.4.1:Numerical Methods for Propagating Uncertainty Across Scales and for Hybrid Stochastic-Deterministic Systems
Abstract
We address an important research area in stochastic multiscale modeling, namely, the propagation of uncertainty across heterogeneous domains characterized by partially correlated processes with vastly different correlation lengths. This class of problems arises very often when computing stochastic PDEs and particle models with stochastic/stochastic domain interaction but also with stochastic/deterministic coupling. The domains may be fully embedded, adjacent, or partially overlapping. The fundamental open question we address is the construction of proper transmission boundary conditions that preserve global statistical properties of the solution across different subdomains. Often, the codes that model different parts of the domains are black box and hence a domain decomposition technique is required. No rigorous theory or even effective empirical algorithms have yet been developed for this purpose, although interfaces defined in terms of functionals of random fields (e.g., multipoint cumulants) can overcome the computationally prohibitive problem of preserving sample-path continuity across domains.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 19, 2023
- Source ID
- W911NF1410425
Entities
People
- George Karniadakis
Organizations
- Army Contracting Command
- Brown University
- United States Army