Stochastic PDEs

Simulations of most physical systems are fundamentally stochastic. Even essentially deterministic systems must be treated stochastically when their parameters, boundary and initial conditions, or forcing functions are under-specified by data. Well-characterized probabilistic estimates are the foundation of simulation-based risk analyses. The Stochastic Partial Differential Equations (SPDEs) project addresses one of the most critical problems in SPDEs: efficient computation of uncertainty as it propagates through the dynamics of non-linear systems. This problem lies at the heart of establishing trust in simulation-based stockpile certification; and in environment, energy, and health security. Quantifying uncertainty is a ubiquitous problem in most analyses and assessments performed at LANL, and in statistical characterization of rare events and of highly heterogeneous random fields.