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<p>Efficient evaluation of geothermal systems is critical for reliable and scalable development. However, conventional workflows are often constrained by the high computational cost of numerical simulations and the limited fidelity and generalizability of surrogate models. Here we present a physics-constrained neural operator framework that enables rapid, high-resolution, and physically consistent system-level evaluation of geothermal performance. By learning the solution operator of governing partial differential equations under physical constraints, the method captures both subsurface dynamics and surface energy production across diverse geological heterogeneity, reservoir conditions, and operational strategies. It achieves an average relative error of 1.76% over more than 7×10⁸ reservoir prediction points and 1.70% for over 6×10<sup>4</sup> target variables, while delivering approximately 1,400-fold acceleration compared to conventional numerical methods. By further integrating modules for power output estimation and economic evaluation, the framework enables consistent techno-economic assessment across multiple geothermal applications. This capability supports rapid ensemble-based analyses, including resource assessment, uncertainty quantification, and multi-objective optimization, providing a scalable pathway for geothermal development.</p>

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A robust physics-constrained neural operator framework for efficient geothermal resource development

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月15日

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  • Zhenqian Xue,
  • Jianfei Bi,
  • Haoming Ma,
  • Zhe Sun,
  • Zhangxing Chen

摘要

Efficient evaluation of geothermal systems is critical for reliable and scalable development. However, conventional workflows are often constrained by the high computational cost of numerical simulations and the limited fidelity and generalizability of surrogate models. Here we present a physics-constrained neural operator framework that enables rapid, high-resolution, and physically consistent system-level evaluation of geothermal performance. By learning the solution operator of governing partial differential equations under physical constraints, the method captures both subsurface dynamics and surface energy production across diverse geological heterogeneity, reservoir conditions, and operational strategies. It achieves an average relative error of 1.76% over more than 7×10⁸ reservoir prediction points and 1.70% for over 6×104 target variables, while delivering approximately 1,400-fold acceleration compared to conventional numerical methods. By further integrating modules for power output estimation and economic evaluation, the framework enables consistent techno-economic assessment across multiple geothermal applications. This capability supports rapid ensemble-based analyses, including resource assessment, uncertainty quantification, and multi-objective optimization, providing a scalable pathway for geothermal development.