Tablets are the most widely used pharmaceutical dosage form, representing over 80% of marketed products, due to their precise dosing, economical production, extended stability, ease of distribution, patient convenience, and ability to mask undesirable tastes (Gohel and Jogani, 2005, Chen et al., 2019). Preferably, tablets are manufactured by direct compression (DC), a process in which the powder blend is first homogeneously mixed and then compressed into tablets without intermediate steps or pretreatment. DC is preferred for its simplicity, cost efficiency, and the absence of water or heat during processing (Armstrong, 2007, Chen et al., 2019). However, successful implementation of DC requires powder mixtures with adequate flow behavior to ensure uniform die filling during tableting, as well as sufficient compactibility and limited elastic recovery to produce mechanically stable tablets. The development of DC formulations remains challenging, as many APIs exhibit poor compactibility (Gohel and Jogani, 2005, Van Snick et al., 2017). To address this issue, formulation development strategies that compensate for any suboptimal properties of the API are essential to achieve the desired tablet strength and to prevent defects such as chipping, capping, and lamination (Jacques and Alexandridis, 2019, de Backere et al., 2021).

The complex tableting process of powder mixtures has already been studied by various authors focusing on compressibility (i.e., tablet porosity as a function of compression force) (Frenning et al., 2009, Mazel et al., 2011, Busignies et al., 2006, Busignies et al., 2012, Polak et al., 2024, Wang et al., 2021, Wünsch et al., 2021, Yu et al., 2020), compactibility (i.e., tablet tensile strength as a function of tablet porosity) (Patel et al., 2011, Polak et al., 2024, Wu et al., 2006, Wang et al., 2021, Wünsch et al., 2021), and tabletability (i.e., tablet tensile strength as a function of compression force) (Wang et al., 2021, Wang et al., 2023, Wang et al., 2024, Wang et al., 2025).

Several researchers focused on the prediction of tensile strength (Dhondt et al., 2022, Borja et al., 2025, Hayashi et al., 2018, Leuenberger et al., 1987, Holman, 1991, Blattner et al., 1990, Amin and Fell, 2004, Hayashi et al., 2017, Hayashi et al., 2020, Escotet-Espinoza et al., 2018). A sufficiently high tensile strength is crucial to ensure that tablets can endure handling during manufacturing and transport. How, it must remain low enough to allow for disintegration upon administration for effective API release (Pitt and Heasley, 2013). The percolation theory is often used to explain the influence of formulation composition on tablet tensile strength and serves as a basis for several prediction approaches (Leuenberger et al., 1987, Holman, 1991, Blattner et al., 1990, Amin and Fell, 2004). However, a key limitation of these models is the need to estimate parameters related to the tabletability properties of the mixture, which prevents their direct application using only the known properties of the constituent materials. A model capable of predicting the tensile strength at a given compaction pressure for powder mixtures directly from the properties of the pure materials would streamline tablet formulation development, saving both time and materials, and would represent a significant step towards digital tablet formulation design (Sun, 2016). To address this limitation, Escotet-Espinoza et al. (2018) have focused on predicting tablet tensile strength by directly integrating experimentally measured material properties into phenomenological models. In this case, model parameters were determined through regression and subsequently captured in empirical relationships. However, these material properties were primarily related to flowability, and the formulation complexity considered remained limited. More tableting-relevant raw material properties were included by Hayashi et al. (2018) and Dhondt et al. (2022). The first study applied a boosted tree model to a dataset of 81 API-containing tablets to predict tensile strength, while the latter used a T-shaped partial least squares (T-PLS) model on a dataset of direct compression experiments. Since the predictive performance of the T-PLS approach was poor, Borja et al. (2025) reanalyzed the same dataset using a probabilistic knowledge-guided artificial neural network. As this data-driven model captures complex, nonlinear relationships between the different factors involved in the process, the predictive accuracy improved (Borja et al., 2025). Nonetheless, these studies only addressed tensile strength at a limited number of compaction forces. Predicting tensile strength across the entire compression range (i.e, the tabletability profile) is of greater practical relevance, as it captures the full relationship between compaction force and mechanical strength. Other studies have applied machine learning techniques to the prediction of tablet tensile strength. Mäki-Lohiluoma et al. (2021) evaluated ridge regression and random forest models to predict both granule particle size distribution and tablet tensile strength from commercial manufacturing data. De Bisshop and Klinken (2023) employed a Long Short-Term Memory (LSTM) framework to predict tablet tensile strength based on process time-series data. Abdelrahman and Klinken-Uth (2025) combined powder label encoding and word embeddings with the Vreeman–Sun tabletability equation (Vreeman and Sun, 2022) in a neural-network framework to predict the tensile strength of powder mixtures, among other critical quality attributes (CQAs). However, predictive performance for previously unseen powders still requires the availability of blend data.

In a strand of modeling that applies mixing rules, Reynolds et al. (2017) proposed a multi-step approach to predict tabletability by first estimating compressibility using the Gurnham equation and volumetric additivity, then predicting compactibility with the Ryshkewitch–Duckworth equation combined with a geometric mean rule, and finally evaluating the predicted vs. the observed tensile strength profiles as a function of compaction pressure (Reynolds et al., 2017, Ryshkewitch, 1953, Gurnham and Masson, 1946). The method was demonstrated on binary and ternary mixtures of excipients, where it successfully predicted mixture properties from those of the individual components. However, when applied to API-containing formulations, Wünsch et al. (2022) reported that the approach did not perform reliably. Tait et al. (2024) systematically evaluated common empirical compression and compaction models across placebo and API-loaded formulations and demonstrated that much of the reported variability in model parameters arises from non-unique fitting solutions rather than actual material differences. By introducing a global optimization framework to populate arithmetic, geometric, and harmonic mixture rules, they showed that consistent tuning parameters can be obtained across formulations, improving predictive stability and generalizability. More recently, Bhagali et al. (2025) added an assessment based on the Vreeman–Sun tabletability equation, which enables quantitative prediction of tabletability profiles through three material-specific parameters (Bhagali et al., 2025, Vreeman and Sun, 2022). By also evaluating different mixing rules to estimate these parameters for binary mixtures (however, not yet employing the global optimization approach described in Tait et al. (2024)), the authors found that a power-law mixing rule mostly outperformed linear and harmonic alternatives, delivering the most accurate predictions across mixtures with diverse mechanical properties. A limitation of the study is that the proposed mixing approach does not account for percolation phenomena, where a component’s influence on mechanical performance becomes dominant when exceeding a critical concentration. Moreover, the study was limited to one API with good compaction behavior. The evaluation of the approach for more divergent APIs would be interesting, especially as APIs are often poorly compactable, which significantly challenges the practical application of these methods (Yu et al., 2020).

In this study, the power-law mixing rule for tabletability parameters was evaluated using four different APIs and one filler. The accuracy of the predicted tabletability of binary mixtures was assessed by comparing the results with predictions made by neural network (NN) model. This model was developed using an extensive tableting database comprising over 200 processed formulations, including binary, ternary, quaternary and quinary blends produced under various process settings. The model links the tabletability of the processed formulations to the applied process settings, the formulation composition and several material-specific properties of the pure components that characterize their compaction behavior, which were determined through individual compaction experiments.