Optimal Transport-Based Data Assimilation Scheme for Individual-Based Models

In this study, a data assimilation scheme for individual-based models (IBMs) based on optimal transport theory is defined and analyzed. When simulating an IBM and acquiring observations of population densities and food concentrations, the assimilation scheme allows the observations to be used for model correction by deriving density fields, performing an ensemble Kalman filter update on the derived fields, and then updating the IBM. The update can be done as a full resampling of the IBM, but this breaks the continuity of individual trajectories. In this study, optimal transport theory is used to design an alternative update method. The algorithm computes transport plans for moving individuals to achieve the target density fields while optimizing transport costs computed as a function of individual movement distances. The performance of the method using the two alternative approaches was analyzed for a synthetic test system. The update method based on optimal transport achieved similar accuracy as a method based on resampling the IBM while also preserving coherent individual trajectories, with the trade-off being a higher computational cost.