The building material stock plays a pivotal role in the circular economy by reducing reliance on virgin resources through material reuse and recovery. Realizing this potential requires accurate mapping of urban material flows, yet such efforts are often hindered by missing material-specific data in cadastral and GIS records. Among bottom-up estimation approaches, Similarity weighting (SW) is a novel method that infers unknown building properties from known samples via similarity-based averaging. While SW addresses the oversimplifications of conventional archetype models, it remains limited by subjective parameter selection, a coverage–accuracy trade-off, and reduced efficacy in high-dimensional contexts—all constraining its generalizability. To overcome these challenges, this study proposes Softmax Similarity Weighting (SoftmaxSW), a reformulation of classical SW method (inverse-distance-weighting) into a probabilistic similarity-based approach. This shift improves generalizability by enabling adaptation to diverse data conditions, enhancing numerical stability, and ensuring consistent performance across varying feature dimensions, while maintaining high coverage and accuracy. Additional branches integrate a radius scaling function to account for real-world interval-dependent shifts, such as temporal variations in material usage patterns. The method is applied to building replacements (BR) in Zurich City (2001–2019), estimating structural material use and embodied carbon emissions for 6,115 demolished and constructed buildings. Validation on 48 Swiss sample buildings shows 100% theoretical applicability and over 75% accuracy. SoftmaxSW matches the overall performance of Support Vector Machine and outperforms it in material-specific predictions. Results highlight slabs and walls, concrete, and multi-residential and office buildings as key areas for circularity within the BR context. Overall, SoftmaxSW provides a generalizable bottom-up framework for scalable interpolation of localized assessments, including material quantities and carbon emissions, and further extends to technological performance and other context-specific aspects relevant to urban-scale applications.

(Published paper)Ye, J. Softmax Similarity Weighting for Bottom-up Building Stock Modelling: Application to Building Replacements in Zurich (2001–2019). In: Huuhka, S. (Ed.). Circularity in the Built Environment: Proceedings of the 2025 conference held in Tampere, Finland, September 16-18 2025. Tampere: Tampere University.