硅酸盐学报

利用工业固废作为辅助胶凝材料部分替代水泥熟料可有效降低能耗和碳排放，开发了大掺量矿渣/粉煤灰水泥、超硫酸盐水泥等胶凝材料体系，实现了工业固废的高效利用、变废为宝。然而，仍有海量堆存赤泥、煤矸石等工业固废尚未得到有效利用，在制备胶凝材料时，普遍面临活性低、成分/性能波动大等难题。传统试错法难以应对其配比与性能间的复杂关系，而深度学习方法则常受制于小样本问题，且获得的单点最优配比难以适应原料波动。针对上述挑战，提出了一种基于小样本深度学习的胶凝材料配比优化方法，通过构建变分信息瓶颈预测模型，并结合配比可行域进行优化，以提升配比方案对原料波动的适应性。本工作以热活化赤泥替代矿渣制备超硫酸盐水泥为例。结果表明，该方法在小样本条件下成功获得了兼顾抗压强度与碳排放的配比可行域，为性能波动的工业固废在低碳胶凝材料中的应用提供了有效的品质控制方法。

Introduction Cement production is a highly energy and carbon-intensive process, with the industry contributing about 8% of global anthropogenic CO₂ emissions. Industrial solid wastes such as slag, fly ash, red mud, and coal gangue are produced in a large scale and persist in the environment, making their treatment and valorization a challenge. Replacing part of the clinker with supplementary cementitious materials(SCMs) is a proven strategy for lowering emissions. Nevertheless, many industrial solid wastes, such as red mud and coal gangue, remain underutilized due to their low reactivity and high impurity levels, causing a large variability in physicochemical properties. Such characteristics pose challenges for mix design due to complex mix proportion-performance relationships and restricted experimental trials. Deep learning-based mix proportion design achieves a notable success due to its universal approximation capability. However, conventional models, such as deep neural networks, typically require large datasets to achieve robust prediction. Obtaining sufficiently large datasets for such models is highly challenging due to limited experimental trials in mix proportion design. Moreover, those methods output only a single optimal mix, failing to account for variability in physicochemical properties of some solid wastes across sources and batches. To address those problems, this study was to apply few-shot learning to develop a highly accurate and generalizable prediction model. In addition, a feasible-region-based design approach was also proposed to tackle physicochemical properties variability. Finally, a multi-objective optimization method was introduced to quantify trade-offs between carbon emission reduction and structural performance. Furthermore, the proposed few-shot learning-based mix design method could optimize the feasible mix region for red mud-based supersulfated cement. This optimization demonstrated the effectiveness and applicability of the proposed methodology. Methods This research was to use few-shot deep learning to construct the performance prediction models for novel solid waste cementitious materials. A variational information bottleneck(VIB) neural network was developed, exhibiting superior generalization under small-sample conditions, compared with conventional networks. This model incorporated specialized preprocessing strategies addressing multicollinearity problems. A custom activation function for compressive strength prediction was designed, along with regularization techniques such as the Batch Normalization and Dropout. To address challenges from variability in physicochemical properties, a feasible-region-based mix design approach was proposed, offering proportion ranges instead of single optimal solutions. This enhanced an adaptability to raw-material variations across batches and sources. Furthermore, a multi-objective optimization method was developed, incorporating carbon-emission factors to obtain mix proportions that could balance compressive strength and environmental benefits. A comprehensive performance metric, the eco-efficiency ratio, defined as 28-d compressive strength divided by total carbon emissions, was introduced, representing the structural performance per unit carbon emission. Results and discussion In this study, the proposed few-shot deep learning-based mix design method is employed to optimize red mud-based supersulfated cement. The results indicate that the proposed model outperforms conventional artificial neural networks(multilayer perceptron, MLP). Furthermore, the model maintains consistently small training-testing error gaps, indicating an effective overfitting prevention. Validation using ten verification mix proportions shows that the proposed model achieves lower prediction errors than the MLP for samples with substantially different mix proportions from the training data, confirming a superior generalization across the entire mix-proportion space. The feasible-region-based mix design approach can identify acceptable proportion ranges from the mix proportion-compressive strength landscape generated by the model. The results indicate that as clinker content increases from 0.1% to 5.0%, acceptable red-mud content gradually decreases, while greater slag proportions contributed to meeting strength requirements. Also, the optimal 28-d compressive strength typically occurs when slag content ranges from 75% to 85% and gypsum content from 10% to 20%, consistent with supersulfated cement formulations, thereby supporting a reliability of the developed compressive-strength prediction model. The acceptable mix-proportion ranges identified from the mix proportion-relative strength landscape indicate that the relative strength declines with increasing clinker content due to the higher carbon-emission factor of clinker. Moreover, the results indicate that the mix proportions yielding the maximum relative strength lay outside the feasible region, because the carbon-emission factor of slag is higher than that of other components, despite its superior reactivity. When producing red mud-based supersulfated cement, it is necessary to choose a mix proportion based on the reactivity of the red mud to balance product performance and carbon-reduction benefits. Conclusions This research demonstrated a potential of few-shot deep learning-based optimization methods for mix-proportion design of solid-waste cementitious materials. A variational information bottleneck-based modeling method was developed, incorporating a specialized preprocessing strategy for mix-proportion data, a tailored activation function for compressive-strength output, and regularization techniques. A feasible-region-based mix-proportion design method was proposed to address challenges from the variability of physicochemical properties, offering adaptable solutions for different sources and batches of solid waste rather than single optimal designs. The proposed method was applied to optimize a red mud-based supersulfated cement. The results indicated that at 30% red mud content, the 28-d compressive strength could remain comparable to the control group without red mud. At 40% content, the optimal carbon emission benefit was achieved, while meeting the 28-d compressive strength requirements. This study could validate the effectiveness of the proposed few-shot performance prediction model and the feasible region-based mix proportion optimization method.