Dynamic mode decomposition for water-energy-food nexus modelling: Data-driven predictions of policy impacts

The Water-Energy-Food (WEF) Nexus is high-dimensional and sensitive to control inputs, such as policy changes. Constructing Nexus models to predict policy impacts is time consuming, and the temporal resolution of the available data is often coarse, limiting the use of many data-driven methods. We investigated the applicability Dynamic Mode Decomposition with control (DMDc) as a method of performing policy impact predictions. A high-resolution System Dynamics Model (SDM) of the Nexus in Latvia was used to simulate the impacts of different policies on the Nexus at annual resolution between 2000 and 2050 (m=50 snapshots). This simulated data was used to assess how well DMDc could reconstruct policy impacts based on data alone. To obtain numerically stable DMDc models with just 50 snapshots, linear interpolation was used to artificially inflate the data to monthly resolution (m=600). Three policies based on the SDM were tested for two different data sizes, small (n=15 variables) and large (n=100). With 5-15 control-policy variables specified, DMDc was able to reconstruct the impacts in both the small and large data sets for two out of the three policies with moderate accuracy (with a Nash-Sutcliffe Efficiency, NSE>0.4). DMDc was able to capture the general trends in the data but not interannual variability. These findings suggests that DMDc shows promise for impact assessments, but policy variables have to be carefully selected. Improvements to the DMDc pipeline that could improve performance and interpretability are discussed, including data pre-processing steps, architectural changes, and model constraints informed by expert- or stakeholder opinion.