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.

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.

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.

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.

As a predominant construction material in modern civil infrastructure (i.e., roads, bridges, ports, and airports), concrete is susceptible to adversing actions such as external loading, freeze–thaw cycling, and salt ingress. These factors readily induce surface spalling and scaling, accelerating service-life deterioration and posing significant safety risks. The existing polymer-modified mortars and epoxy-based systems are commonly employed for the repair and strengthening of concrete structures. An organically modified belite-calcium sulfoaluminate (HB-CSA) cement mortar is adopted in concrete repair projects due to its rapid setting and early strength. However, the performance requirements differ markedly across construction scenarios in low-flow applications (e.g., vertical or overhead placement), the mortar must maintain a low flowability to prevent sagging/run-off during placement, and mechanical performance depends primarily on bond strength, with relatively relaxed demands on compressive and flexural strengths. By contrast, high-flow applications (e.g., pavement repair or large-area casting) require a high flowability to ensure adequate spreading and filling workability. The compressive strength is a principal mechanical target, while the flexural and bond performance must be also satisfied. These divergent demands make it difficult for a single HB-CSA mixture to meet the performance needs of multiple repair scenarios, underscoring the practical importance of multi-scenario mixture-design optimization for HB-CSA repair mortars.

This study was to investigate an organically modified belite-calcium sulfoaluminate (HB-CSA) cement mortar system. Flow spread was employed as a constraint to distinguish high-and low-flow-state scenarios, while 7-d compressive, 7-d flexural, and 7-d bond strengths were taken as the optimization objectives. To address mixture optimization for both flow states, we introduced (i.e., pioneering its use in the cement materials field) a variational-autoencoder-based generative optimization algorithm (VAE-GOA). The method could leverage a generative model to progressively estimate the probability distribution of optimal mixtures over the global design space. In parallel, an adaptive global-exploration strategy prioritized high-potential regions to mitigate premature convergence to local optima, and an iterative optimization scheme further drived the search toward superior solutions. The approach delineated the optimal composition windows and corresponding performance of HB-CSA repair mortars under different flow-state scenarios via visualizing the VAE-GOA–estimated distribution of optimal mixtures. In addition, backscattered electron (BSE) imaging of the interfacial transition zone (ITZ) was also employed to elucidate the mechanisms underlying the improvement in bond performance.

At the outset, the VAE-GOA conducts broad, globally exploratory sampling, while unavoidably covering some low-performing regions, effectively uncovering previously unexplored high-potential areas. As iterations proceed, probability mass progressively concentrates in high-performance regions. The search distribution transitions smoothly from global exploration to local exploitation, reduces attention to low-performing zones, and converges toward a compact subspace containing the best-performing mixtures. These dynamics substantiate the algorithm's intended explore-then-exploit behavior in a multi-constraint design space and effectively mitigate premature convergence to local optima.

Based on two optimization generations and despite strict flowability constraints and limited sampling, the VAE-GOA delivers both macro-level performance gains and a marked expansion of feasible design space. The optimum weighted comprehensive performance is improved by about 20% in the high-flow state group and by >25% in the low-flow state group. The candidates with compressive strength >50 MPa increase from 2 to 6, and those with bond strength >6 MPa increase from 4 to 12, substantially broadening mixture options that meet key targets. For low-flow state scenario, increasing the USCMs is accompanied by a nonlinear decrease in the HPMC, and higher USCMs generally require a lower water–binder ratio (w/b). A practical window of 15%–30% USCMs, 2%–6% Wacker 328, and about 0.1% HPMC at a w/b ratio of 0.22 achieves a low flowability witha high interfacial performance (i.e., mixture L8 attains 48.6 MPa (compressive), 9.2 MPa (flexural), and 6.5 MPa (bond)). For high-flow state scenario, the strength-oriented optimum occurs near about 5% USCMs + 1% Wacker 328 at a w/b ratio of 0.25 (i.e., H7 reaches 63.4 MPa (compressive), 8.3 MPa (flexural), and 4.5 MPa (bond)). For cost-oriented deployment, increasing the USCMs to ~30% with 5% Wacker 328 at a w/b ratio of 0.20 yields a balanced, economical option (i.e., ≈50.7/7.4/6.6 MPa for compressive/flexural/bond). Overall, substituting 15%–30% the USCMs for HB-CSA regulates a flowability and enhances a bond strength as well as reduces production costs by 13%–27%.

Holding the HPMC and w/b ratio roughly fixed while pushing the USCMs beyond 30% (H8 vs. H1) reduces the compressive strength by 14.7 MPa but elevates the bond strength to 6.9 MPa, highlighting a deliberate bond-first Pareto choice. The backscattered electron imaging corroborates this pheoneman. The interfacial transition zone (ITZ) in H8 exhibits a significantly lower porosity and a denser microstructure at the old–new interface, explaining the observed bond enhancement.

In this study, the VAE-GOA could expedite the discovery of high-potential HB-CSA mixtures under strict flow constraints and limited sampling. The comprehensive performance of high-flow state mortars was increased by 20%, and that of low-flow state mortars by >25%. Beyond single best points, the method could yield scenario-specific composition windows and a diverse portfolio choices that practitioners could select from according to the strength, bond, and cost priorities. In particular, low-flow applications were supported by a stable window (e.g., 15%–30% USCMs with 0.1% HPMC and w/b ≈ 0.22), while high-flow placement admited both a strength-oriented option (~5% USCMs + 1% Wacker 328 at w/b = 0.25) and a cost-oriented alternative (30% USCMs + 5% Wacker 328 at w/b = 0.20). The VAE-GOA could be sample-efficient, resilient to local optima, and readily extensible to multi-objective constraints. Looking ahead, coupling the framework with durability targets (e.g., freeze–thaw and chloride ingress), long-term field validation, and uncertainty-aware priors could broaden its applicability to scenario-aware specification and lifecycle-optimized repair design.