  This paper introduces two novel concepts in data-driven turbulence modeling
that enable the simultaneous development of multiple closure models and the
training towards multiple objectives. The concepts extend the evolutionary
framework by Weatheritt and Sandberg (2016), which derives interpretable and
implementation-ready expressions from high-fidelity simulation data. By
assigning a shared fitness value to the evolved closure models and utilizing
the CFD-driven training approach by Zhao et al. (2020), the multi-expression
training concept introduced here is able to account for the coupling between
the trained models, i.e. Reynolds stress anisotropy, turbulent heat flux and
turbulence production correction models. As a second concept, a multi-objective
optimization algorithm is applied to the framework. The extension yields a
diverse set of candidate models and allows a trade-off between the training
objectives after analyzing the training results. In this study, the novel
concepts are applied to a benchmark periodic hills case and a vertical natural
convection flow. The predictions of mean flow quantities are improved compared
to decoupled training strategies with distinct and robust improvements for
strongly coupled momentum and thermal fields. The coupled training of closure
models and the balancing of multiple training objectives are considered
important capabilities on the path towards generalized data-driven turbulence
models.
