mlsanityData to 14 Oct 2026

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

arXiv 2603.12870 ↗First posted 13 Mar 2026math.NA cs.CE cs.LGcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 58 of its 282 references that are in the map. First posted on arXiv 13 Mar 2026.

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58 of 282 references.

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Citing papers per year: 2026: 2.

2 papers.

  1. 2026A Data Fusion Framework for Grounding Aerospace Surrogate Model via Experimental Wind-Tunnel Observationscited by 0
  2. 2026LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Predictioncited by 0