Incremental Transformer for Surrogate-Based Inverse Design of Geopolymer Mixtures

Jul 16, 2026

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Small-data inverse design in engineering informatics is challenging when observations are heterogeneous, mixed-type, and governed by physical relations among design variables. A topology-aware surrogate framework guided by an Incremental Transformer (INCRT) is proposed for physics-constrained inverse design and applied to geopolymer mixture design. The approach combines intrinsic-dimensionality analysis, mixed-variable representation, tabular surrogate prediction, manifold rationalisation, and constrained inverse optimisation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

Introduction

Small-data inverse design challenges

Geopolymer concrete as a case study

Proposed INCRT-guided topology-aware framework

Incremental Transformer for Surrogate-Based Inverse Design of Geopolymer Mixtures Giansalvo Cirrincione 1 , Filippo Grassia 1 ∗ 1 Laboratory of Innovative Technologies (LTI, EA 3899) University of Picardie Jules Verne, Amiens, 80025, Hauts-de-France, France Abstract Small-data inverse design is a recurrent challenge in engineering informatics, particularly when observations are heterogeneous, mixed-type, and constrained by physical relations among design variables. A topology-aware surrogate framework guided by an Incremental Transformer (INCRT) is proposed 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. The case study uses a public benchmark of fly-ash and ground-granulated-blast-furnace-slag geopolymer concrete mixtures with compressive-strength and carbon-emission targets. The high-dimensional design space proves strongly redundant, organising around a smaller number of effective mixture regimes. Forward prediction shows that compressive strength requires nonlinear tabular surrogates, whereas carbon emission is largely determined by mixture composition and recovered accurately by regularised linear models. INCRT therefore serves not as a replacement for strong tabular predictors, but as a topology-aware rationalisation layer supplying prototype regimes and a manifold-support score for inverse design. Three inverse-design strategies are compared: unconstrained surrogate optimisation, physicsconstrained 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 guarantee data support. The topology-aware strategy produces candidate mixtures balancing target compliance, carbon reduction, physical admissibility, and proximity to the learned feasible manifold. The framework is not intended to replace experimental validation, but to provide a decisionsupport methodology for screening credible candidate mixtures from small, mixed, physically constrained engineering datasets. Keywords: physics-constrained inverse design; topology-aware surrogate framework; geopolymer mixture design; small heterogeneous data; manifold rationalisation; incremental transformer. 1 Introduction Many engineering design problems are increasingly supported by data-driven models, yet the datasets available in practical design contexts often remain small, heterogeneous, and physically constrained. This situation is common in material mixture design, where each experiment may require laboratory preparation, curing, destructive testing, and environmental assessment. As a consequence, the available data rarely cover the design space uniformly. Observations usually lie on a restricted subset of physically meaningful recipes, shaped by chemistry, processing constraints, and prior engineering practice. ∗ Corresponding author: Filippo Grassia, [filippo.grassia@u-picardie.fr](filippo.grassia@u-picardie.fr) Geopolymer concrete (GPC) is a representative example. It is widely investigated as a lower-carbon alternative to ordinary Portland cement concrete because aluminosilicate precursors such as fly ash (FA) and ground granulated blast-furnace slag (GGBFS) can be activated by alkaline solutions to form hardened binders (Davidovits, 2015 ; Provis and van Deventer, 2009) . The mechanical performance of GPC mixtures depends on nonlinear interactions among precursor composition, activator chemistry, water content, curing temperature, curing time, and aggregate proportions. At the same time, environmental indicators such as carbon dioxide emission are often computed from constituent quantities and emission factors, and therefore behave more like composition-

FAQs

What problem does the Incremental Transformer (INCRT) address in inverse design?

INCRT acts as a topology-aware rationalisation and out-of-distribution control layer. It constrains inverse design toward physically admissible and data-supported mixture regimes rather than replacing strong tabular forward predictors.

How does the framework handle heterogeneous, mixed-variable engineering data?

It integrates intrinsic-dimensionality analysis and a mixed-variable design-space representation. These elements support a topology-aware surrogate framework that improves credibility of candidate mixtures under small, constrained datasets.

Why is topology-aware physics-constrained optimisation better than unconstrained or physics-only optimisation?

Unconstrained optimisation may match target strength while producing physically invalid or off-manifold candidates. Physics-only constraints do not always guarantee data support. The topology-aware strategy balances target compliance, carbon reduction, physical admissibility, and closeness to the learned feasible manifold.

Jul 16, 2026

Upload by Sage