Fast Modeling Methods for Complex System with Separable Features
This work addresses the problem of slow data-driven modeling for engineers dealing with complex systems, but it is incremental as it builds on existing methods like GP and Eureqa.
The paper tackles the slow convergence of genetic programming for large-scale problems by proposing a method that exploits separability in target models, introducing block and factor detection to reduce search space and using LDSE for optimization, showing it is more effective and efficient than Eureqa in all tested cases.
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.