Manufacturing process optimisation usually amounts to searching optima in high-dimensional parameter spaces. In industrial practice, this search is most often directed by human-subjective expert judgment and trial-and-error experiments. In contrast, high-fidelity simulation models in combination with general-purpose optimisation algorithms, e.g. finite element models and evolutionary algorithms, enable a methodological, virtual process exploration and optimisation. However, reliable process models generally entail significant computation times, which often renders classical, iterative optimisation impracticable. Thus, efficiency is a key factor in optimisation. One option to increase efficiency is surrogate-based optimisation (SBO): SBO seeks to reduce the overall computational load by constructing a numerically inexpensive, data-driven approximation („surrogate“) of the expensive simulation. Traditionally, classical regression techniques are applied for surrogate construction. However, they typically predict a predefined, scalar performance metric only, which limits the amount of usable information gained from simulations. The advent of machine learning (ML) techniques introduces additional options for surrogates: in this work, a deep neural network (DNN) is trained to predict the full strain field instead of a single scalar during textile forming („draping“). ... mehrResults reveal an improved predictive accuracy as more process-relevant information from the supplied simulations can be extracted. Application of the DNN in an SBO-framework for blank holder optimisation shows improved convergence compared to classical evolutionary algorithms. Thus, DNNs are a promising option for future surrogates in SBO.