Incremental Transformer for Surrogate-Based Inverse Design of Geopolymer Mixtures

2026-07-12

AI Summary

This study addresses the challenging inverse design problem of geopolymer formulations characterized by limited data, heterogeneous mixed-variable inputs, and stringent physical constraints. To tackle this, the authors propose a topology-aware surrogate framework that integrates intrinsic dimensionality analysis, mixed-variable representation, a nonlinear tabular surrogate model, and an Incremental Transformer (INCRT). Serving as a rationalization layer, INCRT identifies the feasible formulation manifold and provides prototype mechanisms along with manifold support scores. Coupled with constrained optimization, the framework simultaneously optimizes compressive strength, carbon emission reduction, and data-driven support while ensuring physical feasibility. Experiments on a fly ash–slag-based geopolymer dataset demonstrate that the proposed method efficiently generates candidate formulations that satisfy multiple objectives and closely adhere to the physically feasible manifold.

Abstract

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.

Problem

• inverse design
• small-data
• physics-constrained
• geopolymer mixtures
• mixed-type data

Innovation

• Incremental Transformer
• surrogate-based inverse design
• topology-aware optimization
• geopolymer mixtures
• manifold rationalisation