NERSC Initiative for Scientific Exploration (NISE) 2011 Awards

Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale

Nicholas Zabaras, Cornell University

Associated NERSC Project: Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale (m1182)

Predictive modeling of multiscale and multiphysics systems requires accurate data-driven characterization of the input uncertainties and understanding how they propagate across scales and alter the final solution. We address three major current limitations in modeling stochastic systems: (1) Integration of multiscale models with stochastic analysis poses unique mathematical and computational challenges, and (2) The dimensionality of the stochastic space is very high, (3) The stochastic inputs are rarely derived from experimental data and the underlying physics. The integration of the multiscale and stochastic nature of the problems of interest is addressed with the development of stochastic coarse graining methods. The curse of dimensionality in the solution of the high-dimensional stochastic multiscale PDE systems under consideration is addressed with the construction of low-complexity surrogate models. Input uncertainties are modeled by data-driven multiscale adaptive nonlinear low-order models. We are currently at the dawn of a new stochastic simulation era, and computationally tractable low-complexity surrogate models will play a significant role in the future in harnessing and controlling complex stochastic systems. Our integrated methodology involves concepts from manifold learning, high dimensional model representations (HDMR) in stochastic space, sparse grid stochastic collocation, spectral and hybrid approaches, stochastic multiscale mathematics (stochastic homogenization theory), non-linear model reduction of SPDEs, scalable multigrid methods, Bayesian multiscale estimation and scalable parallel algorithms. The integrated methodology will be based on a scalable multilevel parallelism approach (which incorporates both task and data parallelism) and will be implemented using the Global Arrays (GA) programming model. We will exploit the GA hierarchical processor group concept to extend the scalability to larger number of processors on current petascale and emerging exascale architectures, which allows for tractable collocation-based approaches. The proposed computational thinking can be applied to many areas as uncertainty and model reduction cut across all disciplines in physical and biological sciences, from climate modeling to systems biology.

We propose to demonstrate the new approach in two important class of problems: transport processes in random geological media and predicting the response of materials with random microstructures. In particular, two critical applications of importance to the mission of the DOE will be considered: (a) CO2 geological sequestration with emphasis on mineral dissolution/precipitation and pore clogging under CO2 injection and (b) predictive modeling of void/gas bubble evolution, volume swelling, and performance of irradiated materials of interest to the next generation nuclear reactor design.