Symbolic Regression for Space Applications: Differentiable Cartesian Genetic Programming Powered by Multi-objective Memetic Algorithms
This work addresses the need for interpretable regression models in space applications, offering an incremental improvement over existing symbolic regression methods.
The paper tackled the problem of learning unknown numerical constants in symbolic regression by proposing a multi-objective memetic algorithm with differentiable Cartesian Genetic Programming, showing it is competitive or outperforms black-box models in space applications like Mars express thermal power estimation and star age determination.
Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible free form equations that can be constructed from elementary algebraic functions. While explicit mathematical functions can be rediscovered this way, the determination of unknown numerical constants during search has been an often neglected issue. We propose a new multi-objective memetic algorithm that exploits a differentiable Cartesian Genetic Programming encoding to learn constants during evolutionary loops. We show that this approach is competitive or outperforms machine learned black box regression models or hand-engineered fits for two applications from space: the Mars express thermal power estimation and the determination of the age of stars by gyrochronology.