Use of Dynamic Mode Decomposition for the reconstruction of contaminant release history

The design of effective remediation actions is crucial to protect human health and the environment against the risks posed by aquifer contamination. To improve the predictions of plume properties and the assessment of the efficiency of remediation strategies, much effort has been spent to model subsurface transport processes. One of the most challenging components of the analysis is the identification of the sources of groundwater contamination, which involves the estimation of both locations of the contaminant release and its temporal history. This inverse-modeling task must deal with the complexity of flow path in the aquifer, while contending with the sparsity (both in space and time) of observations of solute concentration. Subsurface heterogeneity and data scarcity require the use of computationally expensive probabilistic methods to solve this inverse problem. We present dynamic mode decomposition (DMD) as an alternative tool to reduce the computational burden of contaminant source identification. DMD is a data-driven, equation-free technique able to interpret the behavior of a system and generate a computationally efficient reduced-order model of the system behavior directly from the data. The method is based on singular value decomposition and consists of a regression of spatially distributed data, collected from a dynamical system at multiple times, onto locally linear dynamics. It allows one to discern dominant spatiotemporal patterns in the dynamical system behavior. We use DMD algorithms to recombine these structures to get system states back in time and reconstruct the contaminant release history.