*Article* **Towards Generative Design of Computationally Efficient Mathematical Models with Evolutionary Learning**

**Anna V. Kalyuzhnaya \*, Nikolay O. Nikitin, Alexander Hvatov, Mikhail Maslyaev, Mikhail Yachmenkov and Alexander Boukhanovsky**

> Nature Systems Simulation Lab, National Center for Cognitive Research, ITMO University, 49 Kronverksky Pr., 197101 St. Petersburg, Russia; nnikitin@itmo.ru (N.O.N.); alex\_hvatov@itmo.ru (A.H.); mikemaslyaev@itmo.ru (M.M.); mmiachmenkov@itmo.ru (M.Y.); boukhanovsky@mail.ifmo.ru (A.B.) **\*** Correspondence: anna.kalyuzhnaya@itmo.ru

> **Abstract:** In this paper, we describe the concept of generative design approach applied to the automated evolutionary learning of mathematical models in a computationally efficient way. To formalize the problems of models' design and co-design, the generalized formulation of the modeling workflow is proposed. A parallelized evolutionary learning approach for the identification of model structure is described for the equation-based model and composite machine learning models. Moreover, the involvement of the performance models in the design process is analyzed. A set of experiments with various models and computational resources is conducted to verify different aspects of the proposed approach.

> **Keywords:** generative design; automated learning; evolutionary learning; co-design; genetic programming
