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Abstract Surrogate models have several uses in engineering design, including speeding up design optimization, noise reduction, test measurement interpolation, gradient estimation, portability, and protection of intellectual property. Traditionally, surrogate models require that all training data conform to the same parametrization (e.g., design variables), limiting design freedom and prohibiting the reuse of historical data. In response, this article proposes graph-based surrogate models (GSMs) for trusses. The GSM can accurately predict displacement fields from static loads given the structure’s geometry as input, enabling training across multiple parametrizations. GSMs build upon recent advancements in geometric deep learning, which have led to the ability to learn on undirected graphs: a natural representation for trusses. To further promote flexible surrogate models, this article explores transfer learning within the context of engineering design and demonstrates positive knowledge transfer across data sets of different topologies, complexities, loads, and applications, resulting in more flexible and data-efficient surrogate models for trusses.