Abstract. We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic regression, dCGP offers a new approach to the long unsolved problem of constant representation in GP expressions. On several problems of increasing complexity we find that dCGP is able to find the exact form of the symbolic expression as well as the constants values. We also demonstrate the use of dCGP to solve a large class of differential equations and to find prime integrals of dynamical systems, presenting, in both cases, results that confirm the efficacy of our approach.

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The preliminary mission design of spacecraft missions to asteroids often involves, in the early phases, the selection of candidate target asteroids. The final result of such an analysis is a list of asteroids, ranked with respect to the necessary propellant to be used, that the spacecraft could potentially reach. In this paper we investigate the sensitivity of the produced asteroids rank to the employed trajectory model in the specific case of a small low-thrust propelled spacecraft beginning its journey from the Sun-Earth L2 Lagrangian point and heading to a rendezvous with some near-Earth asteroid. We consider five increasingly complex trajectory models: impulsive, Lambert, nuclear electric propulsion, nuclear electric propulsion including the Earth's gravity, solar electric propulsion including the Earth's gravity and we study the final correlation between the obtained target rankings. We find that the use of a lowthrust trajectory model is of great importance for target selection, since the use of chemical propulsion surrogates leads to favouring less attractive options 19% of times, a percentage that drops to 8% already using a simple nuclear electric propulsion model that neglects the Earth's gravity effects and thrust dependence on the solar distance. We also find that for the study case considered, a small interplanetary CubeSat named M-ARGO, the inclusion of the Earth's gravity in the considered dynamics does not affect the target selection significantly.

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