The pharmaceutical industry is striving towards pharma 4.0 and continuous manufacturing. This move implies the need for high-quality predictive models for simulation and optimisation problems both for unit operations as well as for plant-wide scenarios. In these continuous production lines, much of the measurement data can be expressed as a distribution, e.g. a particle size distribution. Currently, these measurements are reduced to some characteristic and most of the information content is ignored. As such, a non-linear distribution-agnostic data-driven model framework is proposed to leverage the information content: Kernel Mean Embedding (KME). KME translates a distribution to a point in a high-dimensional feature space while retaining all information of the distribution, and being computationally efficient. These mean embeddings can be used for representation, visualisation, regression and optimisation problems. Extensions to the theory are proposed to create informative monitoring tools, to make prediction models with complex multi-dimensional distributions, to add uncertainty to the model predictions and to add the concept of statistical significance to KME. Finally, these extensions are used to solve optimisation problems: how to optimally select materials to attain certain target quality attributes? How to interpolate between formulations or how to perform experimental design with particular limitations?