Fast Modeling Methods for Complex System with Separable Features

TL;DR

This paper introduces a novel modeling approach leveraging separability in engineering equations, significantly reducing search space and improving efficiency over traditional genetic programming methods.

Contribution

The paper develops a mathematical framework for generalized separable systems and proposes a block and factor detection method to enhance modeling efficiency.

Findings

The new method outperforms Eureqa in accuracy and speed.

It effectively decomposes complex models into minimal blocks and factors.

Experimental results demonstrate superior efficiency and effectiveness.

Abstract

Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large number of variables. Fortunately, in many applications, the target models are separable in some sense. In this paper, we analyze different types of separability of some real-world engineering equations and establish a mathematical model of generalized separable system (GS system). In order to get the structure of the GS system, two concepts, namely block and factor are introduced, and a special method, block and factor detection is also proposed, in which the target model is decomposed into a number of blocks, further into minimal blocks and factors. Compare to the conventional GP, the new method can make large reductions to the search space. The minimal blocks and factors are optimized and assembled with a global optimization search engine, low dimensional simplex evolution (LDSE). An extensive study between the proposed method and a state-of-the-art data-driven fitting tool, Eureqa, has been presented with several man-made problems. Test results indicate that the proposed method is more effective and efficient under all the investigated cases.