Supervised machine learning (ML) models are frequently trained on large datasets of physics-based simulations with the aim of being applied to experimental data. However, ML models trained on simulated data often struggle to perform on experimental data, because there is a shift in the data caused by experimental effects that might be challenging to simulate. We introduce Exp2SimGAN, an unsupervised image-to-image ML model to match simulated and experimental data. Ideally, training Exp2SimGAN only requires a set of experimental data and a set of (not necessarily corresponding) simulated data. Once trained, it can convert a simulated dataset into one that resembles an experiment, and vice versa. We trained Exp2SimGAN on simulated resolution convolved and unconvolved INS spectra. Consequently, Exp2SimGAN can perform a resolution convolution and deconvolution of simulated two- and three-dimensional INS spectra. We demonstrate that this is sufficient for Exp2SimGAN to match simulated and experimental INS data, enabling the analysis of experimental INS data using supervised ML, which was previously not possible. Finally, we provide a domain of application measure for Exp2SimGAN, allowing us to assess the likelihood that Exp2SimGAN will be successful on a specific dataset. Exp2SimGAN is a step towards the analysis of experimental data using supervised ML models trained on physics-based simulations.