ABSTRACT In astronomy, neural networks are often trained on simulation data with the prospect of being used on telescope observations. Unfortunately, training a model on simulation data and then applying it to instrument data leads to a substantial and potentially even detrimental decrease in model accuracy on the new target data set. Simulated and instrument data represent different data domains, and for an algorithm to work in both, domain-invariant learning is necessary. Here, we employ domain adaptation techniques – Maximum Mean Discrepancy as an additional transfer loss and Domain Adversarial Neural Networks – and demonstrate their viability to extract domain-invariant features within the astronomical context of classifying merging and non-merging galaxies. Additionally, we explore the use of Fisher loss and entropy minimization to enforce better in-domain class discriminability. We show that the addition of each domain adaptation technique improves the performance of a classifier when compared to conventional deep learning algorithms. We demonstrate this on two examples: between two Illustris-1 simulated data sets of distant merging galaxies, and between Illustris-1 simulated data of nearby merging galaxies and observed data from the Sloan Digital Sky Survey. The use of domain adaptation techniques in our experiments leads to an increase of target domain classification accuracy of up to ${∼ }20{{\ \rm per\ cent}}$. With further development, these techniques will allow astronomers to successfully implement neural network models trained on simulation data to efficiently detect and study astrophysical objects in current and future large-scale astronomical surveys.