Objective.This study explores the use of neural networks (NNs) as surrogate models for Monte-Carlo (MC) simulations in predicting the dose-averaged linear energy transfer (LET d ) of protons in proton-beam therapy based on the planned dose distribution and patient anatomy in the form of computed tomography (CT) images. As LET d is associated with variability in the relative biological effectiveness (RBE) of protons, we also evaluate the implications of using NN predictions for normal tissue complication probability (NTCP) models within a variable-RBE context. Approach.The predictive performance of three-dimensional NN architectures was evaluated using five-fold cross-validation on a cohort of brain tumor patients ( n= 151). The best-performing model was identified and externally validated on patients from a different center ( n= 107). LET d predictions were compared to MC-simulated results in clinically relevant regions of interest. We assessed the impact on NTCP models by leveraging LET d predictions to derive RBE-weighted doses, using the Wedenberg RBE model. Main results.We found NNs based solely on the planned dose distribution, i.e. without additional usage of CT images, can approximate MC-based LET d distributions. Root mean squared errors (RMSE) for the median LET d within the brain, brainstem, CTV, chiasm, lacrimal glands (ipsilateral/contralateral) and optic nerves (ipsilateral/contralateral) were 0.36, 0.87, 0.31, 0.73, 0.68, 1.04, 0.69 and 1.24 keV  µm -1, respectively. Although model predictions showed statistically significant differences from MC outputs, these did not result in substantial changes in NTCP predictions, with RMSEs of at most 3.2 percentage points. Significance.The ability of NNs to predict LET d based solely on planned dose distributions suggests a viable alternative to compute-intensive MC simulations in a variable-RBE setting. This is particularly useful in scenarios where MC simulation data are unavailable, facilitating resource-constrained proton therapy treatment planning, retrospective patient data analysis and further investigations on the variability of proton RBE.