Equation discovery using mode extraction via singular value decomposition

Abstract

Abstract Many studies have been conducted to elucidate unknown input/output systems based on measured data obtained from experiments and observations. Specifically, neural networks, which have been significantly developed in recent years, can be used for equation discovery. However, the identified networks are considerably large and difficult to understand. Many studies have been conducted on mathematical expressions that are easy to understand; however, there is a paucity of studies on methods to determine a simple equation by eliminating unnecessary terms. In this study, we propose a novel method for identifying unknown equations using mode extraction via singular value decomposition. In this method, the “process of improving the precision of an equation” and the “process of deleting unnecessary terms” are alternately iterated based on singular value decomposition. We confirm the applicability of the proposed method via a sample problem on cantilever deflection. Therefore, the proposed method can accurately determine an equation of an input/output system composed of only essential terms (i.e., excluding unnecessary terms) from training data.

Keywords

• equation discovery
• inverse analysis
• singular value decomposition