Incremental Transformer for Surrogate-Based Inverse Design of Geopolymer Mixtures

Research Approach

This paper addresses the challenge of inverse design in engineering, specifically for geopolymer concrete (GPC) mixtures where datasets are small, heterogeneous, and physically constrained. The authors propose a framework that separates forward prediction from design-space exploration. While traditional surrogate models focus solely on minimizing the error between predicted and target properties, this approach adds two critical filters: physical admissibility and manifold support. The latter is powered by an Incremental Transformer (INCRT), which identifies prototype mixture regimes to ensure that new candidate designs remain within the bounds of experimentally credible data.

Methodology

The workflow consists of four distinct layers. First, the researchers perform intrinsic-dimensionality analysis to confirm that the 19-dimensional design space is highly redundant and organized around specific mixture regimes. Second, they train separate surrogate models: nonlinear tree-based models for compressive strength and regularized linear models for carbon emissions. Third, the INCRT architecture acts as a rationalization layer, providing a manifold-support score that quantifies how close a candidate recipe is to observed data. Finally, the framework compares three optimization strategies: unconstrained, physics-constrained, and the proposed topology-aware physics-constrained optimization.

In small-data engineering, standard optimization often produces "mathematical artifacts"—recipes that appear optimal to a model but are physically impossible or represent dangerous extrapolations. By integrating topology-aware constraints, this framework allows engineers to screen for candidate mixtures that balance performance targets (like strength) with sustainability goals (like carbon reduction) while maintaining physical and data-driven credibility. This methodology provides a robust decision-support tool for material discovery where experimental validation is costly and time-consuming.