Estimation of Explanatory Variables Related to Unknown Mechanisms Based on Residual Models

Abstract

In this study, we propose a method to estimate explanatory variables associated with unknown mechanisms in a given system. Our approach utilizes an approximate physical model, denoted as Mp, which interprets causal variables as explanatory variables and outcome variables as objective variables. Alongside Mp, we employ a statistical residual regression model,Mr, to estimate the residuals between the predictions of Mp and the actual observed values. As Mr is designed to account for the residuals that $M_p$ fails to capture, it inherently contains information regarding the unknown mechanisms of the target structure. Consequently, variables with significant importance in Mr are likely indicators of these mechanisms. When applied to a rainwater storage tank simulation, our method not only successfully identified the explanatory variables linked to the unknown mechanisms but also enhanced the accuracy of the objective variable predictions.