Digital twins may play a transformative role in planning and operation of energy systems. Inspired by [1], we propose that a useful digital twin for energy systems should be able to (i) reproduce historical behaviour, (ii) predict future behaviour, (iii) prescribe future control strategies, and (iv) describe physical properties of the system. A purely data-driven approach would likely achieve (i) and possibly (ii) and (iii) given that the data spans a sufficiently broad set of scenarios but will fail to achieve (iv) in any way meaningful to humans. On the other hand, the degree to which a purely physics-based approach can achieve (i)-(iii) is directly dependent on how well it describes the physical system parameters (iv), which in turn is up to us as modellers. In this work, we outline a hybrid approach: Given a physical system, we construct a low-fidelity simulation model that represents elementary physics (e.g., conservation laws and constitutive relations) and key spatial characteristics (geometry/topology and averaged spatial properties). Parameters of the model are then tuned so that its output best matches corresponding observations form its physical twin (i)-(ii) [2]. Key to this is a fully differentiable simulator framework powered by automatic differentiation, enabling computation of gradients of the mismatch and thereby powerful gradient-based optimization. The same methods enable control optimization and hence prescriptive abilities (iii), and given sufficiently good initial guesses and appropriate constraints, the resulting digital twin may also provide a good description of the physical system parameters (iv). Using the open-source, fully differentiable JutulDarcy.jl simulator [3], we demonstrate how the method can be applied to digital twinning of underground thermal energy storage (UTES), where information about system parameters is sparse and highly uncertain, but measurements of system responses (e.g., energy output from a given production strategy) are abundant. We quantify how well it achieves properties (i)-(iv) and investigate strategies for updating parameters as new data become available.