Projects
Advancing Subsurface Characterization via Ensemble Nonlinear Data assimilation (ASCEND)
Abstract. The subsurface plays a critical role in confronting the challenges of a changing climate. It provides a safe source of drinking water amidst increasingly frequent droughts, and is a keystone of the energy transition through geothermal engineering and hydrogen storage. Despite its importance, insights into this complex environment are scarce, limiting our ability to fully characterize it. The resulting uncertainties demand careful statistical analysis to inform scientifically rigorous and societally responsible subsurface operations. Unfortunately, data assimilation remains challenging in subsurface systems. The statistical paradigm is divided between methods that are either efficient but simplistic (linear), or powerful but intractable (fully nonlinear). The consequences are over-simplification and incompleteness, respectively, which compromise our predictions and decision support, and thus impede geoscientific progress. In this project, I strive to bridge this methodological divide. The key to this is ensemble transport, an innovative statistical method with great capacity for customization. This allows me to create a data assimilation algorithm that shapes itself to the system’s demands, becoming as simple as possible and as complex as necessary. At present, ensemble transport is not yet applicable in high-dimensional subsurface systems. To change this, I will exploit two important features: First, I will advance grid-informed graph detection methods to efficiently discover the system’s web of variable inter-dependencies. Exploiting the resulting conditional independencies ensures scalability to high dimensions. Second, I will develop an adaptation algorithm that identifies an optimal individual degree of nonlinearity for each of the remaining dependencies. This improves statistical analyses and optimizes computational efficiency. Together, both research avenues combine into an efficient adaptive nonlinear data assimilation framework that will permit more precise uncertainty quantification, risk analysis, and stochastic forecasting in complex subsurface systems. Since this project tackles fundamental methodological limitations, I anticipate impact not only in subsurface research, but across the geosciences.
Towards sequential Bayesian inference through transport maps for high-dimensional environmental systems
Abstract. Hydrogeology is among the most challenging subjects for uncertainty quantification. The secure provision of drinking water and irrigation demands knowledge of subsurface properties only sparsely informed by direct measurements. Consequently, meaningful predictions have to account for the manifold sources of uncertainty prevailing in the subsurface.Unfortunately, the numerical complexity of distributed groundwater models and their resulting computational demand is a significant obstacle for most uncertainty quantification methods. Monte Carlo Markov Chains (MCMC) are inefficient in high-dimensional parameter spaces, and computationally economic techniques like the Ensemble Kalman Filter are generally based on limiting assumptions which make it difficult to account for more complex sources of uncertainty.However, recent advances in the field of statistics yielded a new class of statistical tools which might prove highly useful for hydrogeology and environmental systems beyond. Instead of sampling the posterior (the remaining uncertainty after optimization) directly, transportation methods optimize a deterministic function which instead maps samples from a simpler distribution to the otherwise analytically intractable posterior. Once obtained, this function permites the generation of as many samples from the posterior as desired at negligible computational cost. This technique does not suffer from ensemble collapse of filter methods and avoids the high computational demand per sample of MCMC methods.The proposed project investigates the potential of such techniques for high-dimensional, complex environmental models. We will investigate their potential first in a synthetic scenario, later in a field-based study. Should their promise hold, these techniques might open a new path for challenging (high-dimensional, nonlinear, non-Gaussian, chaotic) uncertainty quantification in the environmental sciences.