Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives

TL;DR

This paper reviews various surrogate modeling techniques, including physics-based, data-driven, and hybrid approaches, highlighting recent advances and proposing new perspectives for efficient parametric system approximation.

Contribution

It synthesizes established knowledge and recent developments in surrogate modeling, emphasizing hybrid methods and innovative strategies like multi-fidelity and adaptive sampling.

Findings

Comprehensive review of physics-based and data-driven surrogate methods

Identification of effective hybrid modeling strategies

Discussion of advanced techniques like multi-fidelity and adaptive sampling

Abstract

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.