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  • Open Access

Surrogate modeling via factorization machine and Ising model with enhanced higher-order interaction learning

Anbang Wang1,2,*, Dunbo Cai1, Yu Zhang3, Yangqing Huang4, Xiangyang Feng4, and Zhihong Zhang1,†

  • 1Future Science and Technology Research Lab, China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China
  • 2Graduate School of China Academy of Engineering Physics, Beijing 100193, China
  • 3National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
  • 4BrightGene Bio-Medical Technology Co., Ltd, Suzhou 215000, China

  • *Contact author: wanganbang@cmss.chinamobile.com
  • †Contact author: zhangzhihong@cmss.chinamobile.com
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Phys. Rev. Research 8, 013037 – Published 15 January, 2026

DOI: https://doi.org/10.1103/knt1-yd9s

Abstract

Recently, a surrogate model was proposed that employs a factorization machine to approximate the underlying input-output mapping of the original system, with quantum annealing used to optimize the resulting surrogate function. Inspired by this approach, we propose an enhanced surrogate model that incorporates additional slack variables into both the factorization machine and its associated Ising representation, thereby unifying what was by design a two-step process into a single, integrated step. During the training phase, the slack variables are iteratively updated, enabling the model to account for higher-order feature interactions. We apply the proposed method to the task of predicting drug combination effects. Experimental results indicate that the introduction of slack variables leads to a notable improvement of performance. Our algorithm offers a promising approach for building efficient surrogate models that exploit potential quantum advantages.

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Phys. Rev. Research 8, 013037– Published 15 January, 2026
  • Received 23 June 2025
  • Accepted 9 December 2025
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