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The availability of powerful computational resources and general purpose numerical algorithms creates increasing opportunities to attempt flow simulations in complex systems. How accurate are the resulting predictions? Are the mathematical and physical models correct? Do we have sufficient information to define relevant operating conditions? In general, how can we establish error bars on the results? Uncertainty Quantification (UQ) aims at developing rigorous methods to characterize the impact of limited knowledge on quantities of interest. At the interface between physics, mathematics, probability analysis and optimization, and although quite mature in the experimental community, UQ efforts are in their infancy in computational science. UQ is also a fundamental component of model validation and risk assessment.
The UQLab was founded by Prof. Gianluca Iaccarino within the Advanced Scientific Computing (ASC) program sponsored by the US Department of Energy.


Our group is focused on the quantification of uncertainties in computational fluid dynamics. We develop algorithms to make UQ studies less expensive, strategies to estimate uncertainties induced by modeling assumptions. Recently we also focused on design under uncertainty. Below are links to few representative publications; please contact Prof. Iaccarino for more details (jops at stanford dot edu).

  • Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures >>> View Paper
  • A QMU approach for characterizing the operability limits of air-breathing hypersonic vehicles >>> View Paper
  • A least-squares approximation of partial differential equations with high-dimensional random inputs >>> View Paper
  • A simplex-based numerical framework for simple and efficient robust design optimization >>> View Paper

The UQLab at Stanford actively collaborates with:


Qiqi Wang - Uncertainty quantification for unsteady fluid flow using adjoint-based approaches >>> View Thesis
Paul Constantine - Spectral methods for parameterized matrix equations >>> View Thesis
Tonkid Chantrasmi - Pade-legendre method for uncertainty quantification with fluid dynamics applications >>> View Thesis
John Axerio-Cilies - Predicting formula 1 tire aerodynamics: sensitivities, uncertainties and optimization >>> View Thesis
Per Pettersson - Uncertainty quantification and numerical methods for conservation laws >>> View Thesis
Gary Tang - Methods for high dimensional uncertainty quantification: regularization, sensitivity analysis, and derivative enhancement >>> View Thesis
Mike Emory - Estimating model-form uncertainty in Reynolds-averaged navier-stokes closures >>> View Thesis
Akshay Mittal - Uncertainity propogation in multiphysics systems >>> View Thesis
Nicolas Kseib - Data driven and uncertainty aware physical modeling >>> View Thesis
Saman Ghili - Polynomial and rational approximation techniques for non-intrusive uncertainty quantification >>> View Thesis