Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a wide range of applications, including optimisation, control, data assimilation, uncertainty quantification, and emerging digital twin technologies in various fields such as manufacturing, personalised healthcare, smart cities, and sustainability. This article reviews established methodologies for constructing surrogate models exploiting either knowledge of the governing laws and the dynamical structure of the system (physics-based) or experimental observations (data-driven), as well as hybrid approaches combining these two paradigms. By revisiting the design of a surrogate model as a functional approximation problem, existing methodologies are reviewed in terms of the choice of (i) a reduced basis and (ii) a suitable approximation criterion. The paper reviews methodologies pertaining to the field of Scientific Machine Learning, and it aims at synthesising established knowledge, recent advances, and new perspectives on: dimensionality reduction, physics-based, and data-driven surrogate modelling based on proper orthogonal decomposition, proper generalised decomposition, and artificial neural networks; multi-fidelity methods to exploit information from sources with different fidelities; adaptive sampling, enrichment, and data augmentation techniques to enhance the quality of surrogate models.

翻译：代理模型在用户定义的输入参数与输出关注量之间提供紧凑的关联关系，使得复杂参数系统在多查询场景下能够被高效评估。此类能力在广泛的应用领域中至关重要，包括优化、控制、数据同化、不确定性量化，以及制造业、个性化医疗、智慧城市与可持续性等新兴数字孪生技术。本文综述了构建代理模型的现有方法学，这些方法或利用系统控制律与动力学结构的知识（基于物理），或利用实验观测数据（数据驱动），以及融合这两种范式的混合方法。通过将代理模型的设计重新表述为函数逼近问题，现有方法学从以下两个选择角度进行评述：（i）降维基底的选取，以及（ii）合适逼近准则的确定。本文回顾了科学机器学习领域相关的方法学，旨在综合关于以下方面的已有知识、最新进展与新视角：基于本征正交分解、广义本征分解与人工神经网络的降维、基于物理与数据驱动的代理建模；利用多精度信息源的多保真度方法；以及通过自适应采样、模型增强与数据增广技术提升代理模型质量。