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

2026-03-13

AI Summary

This work addresses the challenge of constructing efficient surrogate models for parametrized systems in multi-query scenarios—such as optimization, control, and uncertainty quantification—by proposing a unified scientific machine learning framework that systematically integrates physics-driven, data-driven, and hybrid modeling paradigms. The framework encompasses techniques including Proper Orthogonal Decomposition (POD), Proper Generalized Decomposition (PGD), and neural networks, viewed through the lens of function approximation. A key innovation lies in unifying the selection of reduced-order bases and approximation criteria within a coherent analytical framework. Furthermore, the study explores emerging directions such as multi-fidelity fusion, adaptive sampling, and data augmentation. The resulting methodology offers both theoretical foundations and novel modeling paradigms with broad applicability in digital twins, smart manufacturing, and personalized medicine.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• surrogate modelling
• parametric systems
• physics-based
• data-driven
• multi-query

Innovation

• surrogate modeling
• scientific machine learning
• multi-fidelity methods
• adaptive sampling
• proper orthogonal decomposition