AI 中文总结
针对工程信息学中小数据逆设计难题，提出基于增量变换器的拓扑感知代理框架用于地质聚合物混合物设计，集成多种方法，通过实验比较三种策略，该框架可筛选可信候选混合物，支持而非替代实验验证。
AI 中文摘要
在工程信息学中，当观测数据具有异构性、混合类型且受设计变量间物理关系约束时，小数据逆设计具有挑战性。本文提出了一种由增量变换器（INCRT）引导的拓扑感知代理框架，用于物理约束逆设计，并应用于地质聚合物混合物设计。该方法集成了本征维数分析、混合变量设计空间表示、表格代理预测、基于INCRT的流形合理化和约束逆优化。通过一个基于粉煤灰和矿渣的地质聚合物混凝土混合物的公共基准测试，结果表明高维设计空间存在大量冗余，围绕较少的有效混合物状态组织。抗压强度需要非线性表格代理，而碳排放很大程度上由成分决定，正则化线性模型能很好地恢复。INCRT作为一种合理化层，为逆设计提供原型状态和流形支持分数。比较了三种策略：无约束代理优化、物理约束优化和拓扑感知物理约束优化。拓扑感知策略产生能够平衡目标符合度、碳减排、物理可接受性以及与学习到的可行流形接近度的候选方案。该框架旨在支持从小的、混合的、物理约束的工程数据集中筛选可信的候选混合物，而不是取代实验验证。
英文摘要
Small-data inverse design is challenging in engineering informatics when observations are heterogeneous, mixed-type, and constrained by physical relations among design variables. This work proposes a topology-aware surrogate framework guided by an Incremental Transformer (INCRT) for physics-constrained inverse design, applied to geopolymer mixture design. The method integrates intrinsic-dimensionality analysis, mixed-variable design-space representation, tabular surrogate prediction, INCRT-based manifold rationalisation, and constrained inverse optimisation. Using a public benchmark of fly-ash and slag-based geopolymer concrete mixtures with compressive-strength and carbon-emission targets, the high-dimensional design space proves strongly redundant, organising around fewer effective mixture regimes. Compressive strength requires nonlinear tabular surrogates, while carbon emission is largely determined by composition and well recovered by regularised linear models. INCRT thus acts not as a replacement for tabular predictors but as a rationalisation layer providing prototype regimes and a manifold-support score for inverse design. Three strategies are compared: unconstrained surrogate optimisation, physics-constrained optimisation, and topology-aware physics-constrained optimisation. Unconstrained optimisation can match target strength but may yield physically invalid or off-manifold candidates; physics-only constraints do not always ensure data support. The topology-aware strategy yields candidates balancing target compliance, carbon reduction, physical admissibility, and proximity to the learned feasible manifold. The framework aims not to replace experimental validation but to support screening of credible candidate mixtures from small, mixed, physically constrained engineering datasets.
