Animals have exquisite control of their bodies, allowing them to perform a diverse range of behaviours. How such control is implemented by the brain, however, remains unclear. Advancing our understanding requires models that can relate principles of control to the structure of neural activity in behaving animals. Here, to facilitate this, we built a 'virtual rodent', in which an artificial neural network actuates a biomechanically realistic model of the rat in a physics simulator. We used deep reinforcement learning to train the virtual agent to imitate the behaviour of freely moving rats, thus allowing us to compare neural activity recorded in real rats to the network activity of a virtual rodent mimicking their behaviour. We found that neural activity in the sensorimotor striatum and motor cortex was better predicted by the virtual rodent's network activity than by any features of the real rat's movements, consistent with both regions implementing inverse dynamics. Furthermore, the network's latent variability predicted the structure of neural variability across behaviours and afforded robustness in a way consistent with the minimal intervention principle of optimal feedback control. These results demonstrate how physical simulation of biomechanically realistic virtual animals can help interpret the structure of neural activity across behaviour and relate it to theoretical principles of motor control.