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Inverse Modeling and Uncertainty Quantification

Integration of dynamic response data into subsurface flow models is commonly performed by formulating and solving an inverse problem. For heterogeneous subsurface flow models, the number of unknowns to be estimated is typically overwhelmingly larger than available data, giving rise to an underdetermined inverse problem for which unique solutions cannot be found. Regularization and reduced-order parameterization are two general approaches that incorporate additional information (prior knowledge) to further constrain the solution of underdetermined inverse problems. To account for and quantify the uncertainties in the prior knowledge, observed data, nonlinear mapping from parameter to data space, and the resulting solutions, probabilistic formulations of the inverse problem can be adopted. We develop inverse modeling frameworks for subsurface flow model calibration and uncertainty quantification applications. The main emphasis of our inversion formulations is on identifying the connectivity in important subsurface properties that dominate the flow pattern. As such, we capitalize on feature/pattern-based estimation and imaging methods to better understand and characterize the subsurface environments and the flow patterns in the underlying systems.

An important area of investigation in our lab is solving inverse problem under (global) uncertainty in prior knowledge. In subsurface modeling, prior knowledge is derived from incomplete data and subjective interpretations. Geologic uncertainty is one of the main challenges in developing subsurface flow models, simply because of the lack of convenient access to sufficiently sample these formations. While geologic information/expertise can provide important prior knowledge for constraining the flow and transport models, it inherently entails significant uncertainty not just about the exact location and extent of the existing geologic connectivity features but, more importantly, about the type of geobodies and spatial patterns (e.g., geologic scenario) that exist. In the conventional approach, the geologic scenario (e.g., training image, variogram model, or any other global geologic parameter) is assumed given and used to constrain the solution of the inverse problem. This approach not only prone to introducing significant bias, it also eliminates the opportunity for the geologist to use flow data to resolve or reduce their uncertainty.

We develop inverse modeling formulations that take advantage of available prior geologic knowledge and, at the time, account for the uncertainty in the geologic scenario. By considering the uncertainty in the conceptual geologic model, our methods make it possible to utilize dynamic flow response data to assist geologists in reducing their uncertainty. This step is critical before using the prior knowledge for model calibration. We also investigate and develop novel ensemble-based techniques for practical implementation of probabilistic model calibration and uncertainty quantification. Another research area of great importance is developing joint inverse modeling methods for multi-physics problems, involving flow, transport, deformation, as well as thermal effects and chemical reactions. While coupled flow simulation for predicting the behavior of these systems is currently at the research stage, it is important to simultaneously study and develop joint inverse modeling and uncertainty quantification frameworks.

A few samples of our recent and current research in the above areas include:

  • Sparse representation for inverse modeling and dynamic data integration
  • Pattern-based dynamic data conditioning for complex geosystems
  • Integration of dynamic data for evaluating alternative (uncertainty) geologic scenarios
  • Ensemble-based data integration methods
  • Joint parameter estimation for coupled-physics models involving flow and geomechanical effects
  • Machine learning for low-rank parameterization and efficient dynamic data conditioning

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