The diversity of available material feedstocks, coupled with rigorous performance requirements, complicates the design of ultra-high-performance concrete (UHPC). Here, a Bayesian method for inverse design is first demonstrated from published UHPC data. Materials were represented in a framework of hierarchical machine learning; a fundamental goal in this study was to compare the accuracy and generalizability of models parameterized by compositional variables with those parameterized by latent variables based on empirical models. Data were first modelled by ensemble ridge regression, and miscalibration area (a Bayesian error metric) indicated improved generalizability for models parameterized by latent variables compared to those parameterized by composition. Then, Gaussian process regression based on an expanded feature set was used to predict strength that, counterintuitively, generated higher accuracy for models parameterized by compositional variables (test R 2 = 0.91) than by latent variables (test R 2 = 0.77). However, the latter more accurately predicted the properties of designs produced with untested fine aggregate and predicted novel compositions achieving high compressive strength, consistent with a significant reduction in model miscalibration error. These results demonstrate that latent variables in a Bayesian machine learning framework can provide greater generalizability across the variable space, make robust predictions on untested feedstocks and predict new UHPC compositions with optimal properties. This article is part of the theme issue ‘Frontiers of applied inverse problems in science and engineering’.
Childs et al. (Thu,) studied this question.