Open Access

ARTICLE

CALPHAD-Informed MAP Priors for Cold-Start Composition-Space Partitioning in Active Alloy Design

Haipeng Hu¹, Tao Hong², Junjie Zhu³, Xinjie Yao^4,*, Zhoupeng Guo^5,*, Dahai Xia^6,*

1 College of Artificial Intelligence, Tianjin University of Science and Technology, Tianjin, China
2 China Nuclear Power Engineering Co., Ltd., Beijing, China
3 School of Artificial Intelligence, Xiangyang Polytechnic University, Xiangyang, China
4 Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China
5 School of Automation, Southeast University, Nanjing, China
6 School of Materials Science and Engineering, Tianjin University, Tianjin, China

* Corresponding Authors: Xinjie Yao. Email: ; Zhoupeng Guo. Email: ; Dahai Xia. Email:

Computers, Materials & Continua 2026, 89(2), 15 https://doi.org/10.32604/cmc.2026.086475

Received 31 May 2026; Accepted 27 July 2026; Issue published 15 September 2026

Abstract

Cold-start alloy-design campaigns often have too few labeled compositions to reliably locate phase boundaries for tree-structured composition-space Gaussian process regression (TCGPR). We study a controlled way to incorporate external CALPHAD-like boundary information into this partitioning step. The proposed MP-TCGPR method adds a Gaussian MAP penalty centered on a thermodynamic boundary estimate and uses an adaptive width ${\sigma }_j(N)={\sigma }_0\sqrt{1+N/N_{\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}}$ to reduce prior influence as node-level data accumulate. The revised theory distinguishes asymptotic convergence from convergence rate: a fixed-width prior is also asymptotically negligible under local regularity, whereas the adaptive schedule accelerates finite-sample prior release. Across 900 one-dimensional simulation runs spanning six Al-alloy cross-sections, MP-TCGPR reduces normalized Hausdorff distance at $N_0=10$ from $0.2233\pm 0.2939$ to $0.0613\pm 0.0487$. Additional fixed-width MAP, CALPHAD-only, misspecification, $N_{\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}$, two-dimensional, and active-learning diagnostics show that most cold-start gain comes from a sufficiently accurate thermodynamic prior, while downstream AL benefits are modest in the tested budgets. The method is therefore presented as a reproducible cold-start partitioning strategy whose reliability depends on prior calibration, not as validation of a specific production CALPHAD database.

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Keywords

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