Understanding the behavior of bituminous mixtures is crucial for the design and maintenance of durable road infrastructure. Multiscale modelling, which integrates different scales of analysis, provides a comprehensive approach to predict and analyze the performance of these mixtures. This study presents a multiscale modelling approach using Finite Element (FE) and Machine Learning (ML), specifically Deep Neural Networks (DNN), to simulate and predict the behavior of asphalt binder and asphalt mastic. The Finite Element method was employed to simulate the Dynamic Shear Rheometer (DSR) test, aiming to predict the complex shear modulus (G^*) and phase angle (δ) of the asphalt binder and mastic (asphalt binder + fillers). Concurrently, a DNN model was developed, considering various properties such as aging conditions, physical properties, and DSR test properties. Furthermore, statistical methods including ANOVA, Chi-square, and Random Forest were utilized to identify and rank the most influential parameters affecting the mechanical behavior of the asphalt binder and mastic. Both the FE and ML models demonstrated accurate predictions. The DNN model achieved a high prediction accuracy with an R-squared value of 0.98. The FE model provided physical insights into the behavior of the asphalt binder and mastic under different loading conditions, while the ML model effectively identified and ranked the most significant parameters. This research underscores the potential of integrating FE and ML in multiscale modelling of bituminous mixtures, paving the way for more efficient and sustainable road infrastructure design. The predictive capability of these models is crucial for guiding road authorities and industry professionals in focusing on key factors that influence bitumen's rheological properties. By doing so, they can optimize their data gathering strategies to improve the overall performance of pavements.