A divide and conquer method for symbolic regression

Symbolic regression aims to find a function that best explains the relationship between independent variables and the objective value based on a given set of sample data. Genetic programming (GP) is usually considered as an appropriate method for the problem since it can optimize functional structure and coefficients simultaneously. However, the convergence speed of GP might be too slow for large scale problems that involve a large number of variables. Fortunately, in many applications, the target function is separable or partially separable. This feature motivated us to develop a new method, divide and conquer (D&C), for symbolic regression, in which the target function is divided into a number of sub-functions and the sub-functions are then determined by any of a GP algorithm. The separability is probed by a new proposed technique, Bi-Correlation test (BiCT). D&C powered GP has been tested on some real-world applications, and the study shows that D&C can help GP to get the target function much more rapidly

Elite Bases Regression: A Real-time Algorithm for Symbolic Regression

Symbolic regression is an important but challenging research topic in data mining. It can detect the underlying mathematical models. Genetic programming (GP) is one of the most popular methods for symbolic regression. However, its convergence speed might be too slow for large scale problems with a large number of variables. This drawback has become a bottleneck in practical applications. In this paper, a new non-evolutionary real-time algorithm for symbolic regression, Elite Bases Regression (EBR), is proposed. EBR generates a set of candidate basis functions coded with parse-matrix in specific mapping rules. Meanwhile, a certain number of elite bases are preserved and updated iteratively according to the correlation coefficients with respect to the target model. The regression model is then spanned by the elite bases. A comparative study between EBR and a recent proposed machine learning method for symbolic regression, Fast Function eXtraction (FFX), are conducted. Numerical results indicate that EBR can solve symbolic regression problems more effectively.Comment: The 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2017

Visible-light-driven coproduction of diesel precursors and hydrogen from lignocellulose-derived methylfurans

Photocatalytic hydrogen production from biomass is a promising alternative to water splitting thanks to the oxidation half-reaction being more facile and its ability to simultaneously produce solar fuels and value-added chemicals. Here, we demonstrate the coproduction of H2 and diesel fuel precursors from lignocellulose-derived methylfurans via acceptorless dehydrogenative C 12C coupling, using a Ru-doped ZnIn2S4 catalyst and driven by visible light. With this chemistry, up to 1.04\u2009g\u2009gcatalyst 121\u2009h 121 of diesel fuel precursors (~41% of which are precursors of branched-chain alkanes) are produced with selectivity higher than 96%, together with 6.0\u2009mmol\u2009gcatalyst 121\u2009h 121 of H2. Subsequent hydrodeoxygenation reactions yield the desired diesel fuels comprising straight- and branched-chain alkanes. We suggest that Ru dopants, substituted in the position of indium ions in the ZnIn2S4 matrix, improve charge separation efficiency, thereby accelerating C 12H activation for the coproduction of H2 and diesel fuel precursors

Divide and Conquer: A Quick Scheme for Symbolic Regression

Symbolic regression (SR), as a special machine learning method, can produce mathematical models with explicit expressions. It has received increasing attention in recent years. However, finding a concise, accurate expression is still challenging because of its huge search space. In this work, a divide and conquer (D & C) scheme is proposed. It tries to divide the search space into a number of orthogonal sub-spaces based on the separability feature inferred from the sample data (dividing process). For each sub-space, a sub-function is learned (conquering process). The target model function is then reconstructed with the sub-functions according to their separability patterns. To this end, a separability pattern detecting technique, bi-correlation test (Bi-CT), is also proposed. Note that the sub-functions could be determined by any of the existing SR methods, which makes D & C easy to use. The D & C powered SR has been tested on many symbolic regression problems, and the study shows that D & C can help SR to get the target function more quickly and reliably

Relative contribution ratio: A quantitative metrics for multi-parameter analysis

In many applications, the objective function is determined by several parameters simultaneously. Properly assessing the relative contribution of each parameter can give the decision maker a better understanding of the problem. However, widely used assessing methods are qualitative or semi-quantitative. In this paper, a new concept, relative contribution ratio (RCR), is proposed. The concept follows the idea of proof by contradiction, and estimates the impact of absence of each parameter, based on the fact that the absence of a parameter with more contribution will bring more divergence. Based on surrogate models, a statistical method for calculating RCR is also presented. Numerical results indicate that RCR is capable of analyzing multi-parameter problems, regardless of whether they are linear or nonlinear

Criteria for hypersonic airbreathing propulsion and its experimental verification

Hypersonic airbreathing propulsion is one of the top techniques for future aerospace flight, but there are still no practical engines after seventy years? development. Two critical issues are identified to be the barriers for the ramjet-based engine that has been taken as the most potential concept of the hypersonic propulsion for decades. One issue is the upstream-traveling shock wave that develops from spontaneous waves resulting from continuous heat releases in combustors and can induce unsteady combustion that may lead to engine surging during scramjet engine operation. The other is the scramjet combustion mode that cannot satisfy thrust needs of hypersonic vehicles since its thermos-efficiency decreases as the flight Mach number increases. The two criteria are proposed for the ramjet-based hypersonic propulsion to identify combustion modes and avoid thermal choking. A standing oblique detonation ramjet (Sodramjet) engine concept is proposed based on the criteria by replacing diffusive combustion with an oblique detonation that is a unique pressure-gain phenomenon in nature. The Sodramjet engine model is developed with several flow control techniques, and tested successfully with the hypersonic flight-duplicated shock tunnel. The experimental data show that the Sodramjet engine model works steadily, and an oblique detonation can be made stationary in the engine combustor and is controllable. This research demonstrates the Sodramjet engine is a promising concept and can be operated stably with high thermal efficiency at hypersonic flow conditions. ? 2020 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)