CE Seminar Series – Uncertainty quantification and reduction with conditional Gaussian process models in high dimensional stochastic systems

Ramakrishna Tipireddy, Ph.D.
Research Scientist in the Physical and Computational Sciences Directorate

Pacific Northwest National Laboratory (PNNL)

Abstract
This talk will present a brief introduction to uncertainty quantification (UQ) quantification methods for
high dimensional stochastic PDEs and introduce conditional Gaussian process (GP) models for uncertainty
reduction. The PDE coefficient is represented as a log-normal random field, with the corresponding
Gaussian part modeled as a zero-mean Gaussian process (GP) with appropriate covariance function. The
reduction in uncertainty is achieved by conditioning the GP model on observations of the coefficient at a
few spatial locations. The resulting conditional GP model is then discretized using truncated Karhunen-
Lo`eve (KL) expansion and the stochastic solution of the PDE is computed using Monte Carlo and sparsegrid
collocation methods. Finally, uncertainty in the system is further reduced by adaptively selecting
additional observation locations using two active learning criteria. The first criteria minimizes the
variance of the PDE coefficient, while the second criteria employs approximately minimizes the variance
of the solution of the PDE.
Bio
This talk will present a brief introduction to uncertainty quantification (UQ) quantification methods for
high dimensional stochastic PDEs and introduce conditional Gaussian process (GP) models for uncertainty
reduction. The PDE coefficient is represented as a log-normal random field, with the corresponding
Gaussian part modeled as a zero-mean Gaussian process (GP) with appropriate covariance function. The
reduction in uncertainty is achieved by conditioning the GP model on observations of the coefficient at a
few spatial locations. The resulting conditional GP model is then discretized using truncated Karhunen-
Lo`eve (KL) expansion and the stochastic solution of the PDE is computed using Monte Carlo and sparsegrid
collocation methods. Finally, uncertainty in the system is further reduced by adaptively selecting
additional observation locations using two active learning criteria. The first criteria minimizes the
variance of the PDE coefficient, while the second criteria employs approximately minimizes the variance
of the solution of the PDE.
Civil