Uncertainty Quantification and Data-driven Discovery for High-dimensional Complex Systems with Multimodal Distribution

Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in the modeling, simulation, and optimization of complex systems. The field of uncertainty quantification (UQ) has received an increasing amount of attention. Extensive research efforts have been devoted to it and many novel numerical techniques have been developed. These techniques aim to conduct stochastic simulations for very large-scale complex systems.

In this talk, we will present some effective new ways of dealing with the challenges facing uncertainty quantification community including high-dimensionality, discontinuities, “multi-modal”, model-form uncertainties, UQ for computational-expensive models, UQ for machine learning and data science, etc.

Particularly, a rotation-based compressive sensing technique is developed for high-dimensional UQ problem. Adaptive importance sampling techniques will be discussed for handling multi-modal problems. We demonstrate that we can use emerging, large-scale spatiotemporal data from modern sensors to directly construct and discover, in an adaptive manner, governing equations, even nonlinear dynamics, that best model the system and quantifying the uncertainties in the learning process. Several specific examples of flow and transport in randomly heterogeneous porous media and climate models will be presented to illustrate the main idea of our approaches.