In most archaeological and anthropological applications, time series data on frequency changes of different cultural traits are the only available information about past cultural patterns. Researchers in these fields would benefit from being able to infer information about the underlying evolutionary processes that have produced those frequency changes. This poses a classical inverse problem: we aim to convert available information about changes in variant frequencies into information about the evolutionary processes that have caused those changes, but which cannot be observed directly. We discuss this in the context of social learning and develop a n-variant reaction-diffusion framework that specifies the consequences of different mixtures of learning strategies on the frequencies of cultural variants. We assume that changes in these frequencies are caused by the adoption decisions of individuals and distinguish between the two main adoption mechanisms: social learning, in the form of both directly biased and frequency-dependent transmission; and individual learning.