Data-Driven Corrections of Partial Lotka–Volterra Models

Abstract

In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions—e.g., elimination of hundreds of terms—can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, physical consistency, and robustness to different scenarios—are intended to support reliable predictions under extrapolative conditions.

5. The Community of AIM SQuaREs by Estelle Basor

“…In previous work [7,8], we have seen that reduced models, that only track a subset of L < M variables, can still faithfully represent the dynamics of the complete M × M system. We lacked a theoretical justification for why this should be the case, but now the analysis here can help explain this phenomenon.…”

Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions

“…While the resulting differential equations now include either a derivative or an approximate integral, the numerical solution is rather easily obtained without introducing much numerical complexity. In [31], Morrison provided an expanded investigation into similar AS-type approximate models.…”

Novel predator-prey model admitting exact analytical solution

“…The above deterministic model was created in the third decade of the twentieth century in the field of ecology [1,2]. Almost a century after it was first proposed it still attracts the interest of the scientific community, and an intense research activity has been carried out on this model up to the present day [3][4][5][6][7][8][9][10][11][12].…”