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

Abstraction: Unified review of physics-based, data-driven, and hybrid surrogate models for parametric systems

Key points:

• Frames surrogate construction as a functional approximation problem with two key components: choice of reduced basis and choice of approximation criterion
• Reviews three reduced-basis families: proper orthogonal decomposition (POD via SVD), proper generalized decomposition (PGD), and neural networks
• POD-based surrogates split into intrusive (POD-RB, requires access to governing equations) and non-intrusive (PODI, learns parameter-to-coefficient maps from data only)
• Multi-fidelity methods fuse data from high- and low-cost simulators to build more accurate surrogates with fewer expensive evaluations
• Adaptive sampling and data augmentation strategies discussed as cross-cutting enablers for data-scarce settings
• Applications: optimization, control, uncertainty quantification, inverse analysis, and digital twins in manufacturing, healthcare, and smart cities

Connections: Surrogate Models · Scientific Machine Learning · Proper Orthogonal Decomposition · Reduced Order Models · Multi Fidelity Methods

Source: https://arxiv.org/html/2603.12870