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The performance of a deep learning model on a specific task and dataset depends heavily on its neural architecture, motivating considerable efforts to rapidly and accurately identify architectures suited to the target task and dataset. To achieve this, researchers use machine learning models—typically neural architecture encoders—to predict the performance of a neural architecture. Many state-of-the-art encoders aim to capture information flow within a neural architecture, which reflects how information moves through the forward pass and backpropagation, via a specialized model structure. However, due to their complicated structures, these flow-based encoders are significantly slower to process neural architectures compared to simpler encoders, presenting a notable practical challenge. To address this, we propose FGP, a novel pre-training method for neural architecture encoding that trains an encoder to capture the information flow without requiring specialized model structures. FGP trains an encoder to reconstruct a flow surrogate, our proposed representation of the neural architecture's information flow. Our experiments show that FGP boosts encoder performance by up to 106\% in Precision@1\%, compared to the same encoder trained solely with supervised learning.