Zhang Qinqin ¹, Xu Wenxia ¹, Yu Baocheng ¹, Liang Feng ², Ai Yuming ¹, Chen Guojun ¹

(1. Hubei Engineering Research Center of Intelligent Production Line Equipment, Wuhan Institute of Technology, Wuhan 430205, Hubei, China; 2. State Key Laboratory of Advanced Refractories, Wuhan University of Science and Technology,

Wuhan 430081, Hubei, China)

Extended abstract:

[Background and purposes] Porous alumina ceramics are widely used in high-temperature thermal insulation and structural applications. However, they suffer from an intrinsic contradiction of "high load-bearing versus low thermal conductivity". While introducing mullite fibers can improve the mechanical properties, the complex micro-structure-property relationships, driven by the fibers' high aspect ratio morphology, intrinsic strength and coefficient of thermal expansion (CTE) mismatch with the matrix, make the design process highly challenging. Traditional trial-and-error methods exhibit severe limitations, when conducting collaborative optimization in a high-dimensional parameter space. To overcome these bottlenecks, this study was attempted to construct a closed-loop "prediction-analysis-reverse design" machine learning (ML) framework, aiming at accelerating the discovery and mechanistic understanding of high-performance mullite fiber-reinforced porous alumina ceramics.

[Methods] A data-driven pipeline was established by initially selecting Light Gradient Boosting Machine (LightGBM) as the baseline predictive model. To overcome the inductive bias and overfitting tendencies of pure data-driven models in sparse data intervals (a common issue in small-sample materials datasets), a Physics-Informed Machine Learning (PIML) strategy was proposed. Specifically, classical physical equations, such as the Ryshkewitch equation (for porosity-strength dependence) and the Loeb equation (for porosity-thermal conductivity dependence), were introduced as enhanced features and explicitly embedded into the LightGBM algorithm. Furthermore, SHAP (SHapley Additive exPlanations) was utilized to interpret the black-box model and reveal the underlying mechanisms. Finally, the optimized PIML-LightGBM was employed as a surrogate model and coupled with the Differential Evolution (DE) algorithm to conduct three single-objective inverse optimizations for the ceramic formulations.

[Results] The integration of physical domain knowledge successfully constrained the model, while the constructed PIML-LightGBM model effectively suppressed non-physical oscillations in sparse data regions. The prediction accuracy (R2) for compressive strength and thermal conductivity significantly increased to approximately 0.95 and 0.97, respectively, achieving a perfect unification of high predictive accuracy and physical self-consistency. Relying on the SHAP analysis, the hierarchical impact of various features was quantitatively decoupled, where the pore-forming agent dominates the primary macroscopic properties, temperature regulation acts as a secondary factor and fiber characteristics serve to optimize the fine performance. Mechanistically, the SHAP results elucidated the microscopic regulation mechanism of mechanics and heat transfer, highlighting the bridging effect of the high aspect ratio of mullite fibers and the crucial role of CTE matching between the fibers and the alumina matrix. Driven by the DE algorithm coupled with the surrogate model, an extreme boundary formulation was successfully locked within the physical constraints, obtaining three single-objective boundary formulations, corresponding to maximum porosity of 91.44%, maximum compressive strength of 9.30 MPa and minimum thermal conductivity of 0.070 W·m−1·K−1. Furthermore, experimental validation of the inverse-designed extreme formulations confirmed the high reliability and physical consistency of the model, with relative errors between the predicted and experimental values that are strictly controlled within 6%.

[Conclusions] The proposed PIML-LightGBM framework effectively resolves the overfitting dilemma under small-sample conditions by bridging data-driven algorithms with physical empirical laws. The quantitative interpretability analysis not only reveals the complex synergistic effects of mullite fibers in porous ceramics but also provides deep insights into the microscopic strengthening and thermal insulation mechanisms. Furthermore, the successful implementation of the DE-based reverse design demonstrates that this "prediction-analysis-reverse design" paradigm is a highly efficient and robust scientific tool for the targeted design and advanced development of high-performance porous ceramics and other complex composite materials.

Key words: mullite fiber-reinforced porous alumina ceramics; physics-informed machine learning; LightGBM; interpretability analysis; differential evolution (DE) algorithm