Learning Dynamical Systems Using Standard Symbolic Regression

Abstract

Abstract. Symbolic regression has many successful applications in learning free-form regular equations from data. Trying to apply the same approach to differential equations is the logical next step: so far, however, results have not matched the quality obtained with regular equations, mainly due to additional constraints and dependencies between variables that make the problem extremely hard to tackle. In this paper we propose a new approach to dynamic systems learning. Symbolic regression is used to obtain a set of first-order Eulerian approximations of differential equations, and mathematical properties of the approximation are then exploited to reconstruct the original differential equations. Advantages of this technique include the de-coupling of systems of differential equations, that can now be learned independently; the possibility of exploiting established techniques for standard symbolic regression, after trivial operations on the original dataset; and the substantial reduction of computational effort, when compared to existing ad-hoc solutions for the same purpose. Experimental results show the efficacy of the proposed approach on an instance of the Lotka-Volterra model.

Symbolic regression in materials science

“…It has been shown that symbolic regression can generate ordinary nonlinear partial differential equations for nonlinear coupled dynamical systems 46,68 as well as approximate ordinary differential equations. 69 Meanwhile, it is also often of desire to find conservation laws in physical systems. The ability to unearth conservation laws with symbolic regression goes beyond the aim of materials property predictions and helps researchers establish insight into the materials systems they study.…”

Discovering Unmodeled Components in Astrodynamics with Symbolic Regression

“…When performing symbolic regression, candidate solutions are usually represented as trees, where the terminal nodes (also called "leaves") correspond to constants and variables, and where all the other nodes encode mathematical functions (primitives) [13]. In this work vectors, representing, in a dot add k1 k1 dot k1 X_vec…”

New Method for Constructing a Visibility Graph-Network in 3D Space and a New Hybrid System of Modeling

“…Genetic programming [17] is a collection of methods for the automatic generation of computer programs that solve carefully specified problems, via the core, but highly abstracted principles of natural selection. The organisms that undergo adaptation are in fact mathematical expressions (models) for the surface porosity of hardened Figure 12.…”