Coupling between mechanics and diffusion of physical or chemical species plays a critical role in many engineering problems: concrete and composite structures subject to environmental conditions, geomechanics, energy storage systems (batteries), biomechanics, . . . Complex interactions between mechanics and diffusion and/or different phases in heterogeneous materials can lead to effective macroscopic behaviour which is difficult to represent through classical models (i.e. deriving from Fick’s law). In the linear case (small perturbations from an equilibrium state), model reduction techniques allow deriving explicit macroscopic constitutive equations through upscaling. The situation becomes much more complex when considering non-linearities (material and/or geometrical). In that case, data-driven models may become an interesting alternative, as they avoid formulating explicit models, provided data is available. Constitutive data may for example be obtained from finer scale numerical models, as explored in the work of Waseem et al. (2021). In this presentation, we will discuss on how to extend this previous work to more complex, potentially history-dependent, material response, by formulating a data-driven approach in extended constitutive spaces including strain, stress, concentration, flux, chemical potential and its gradient, plus history variables (rates or others). The methodology will be illustrated on numerical examples, in 1D and 2D settings.