A surrogate model — also called a metamodel, emulator, or response surface — is a fast approximation of an expensive computational simulation, trained on a limited number of simulation runs. It enables probabilistic analysis, optimization, and real-time decision-making that would be infeasible with the original simulation.
A surrogate model — also called a metamodel, response surface, or emulator — is a computationally cheap approximation of an expensive simulation. The motivation is simple: many engineering simulations (finite element analysis, nonlinear response history analysis, computational fluid dynamics) require minutes to hours to run, making them impractical for applications that require thousands or millions of evaluations — probabilistic analysis, optimization, sensitivity studies, real-time decision support, or Monte Carlo simulation. A surrogate model is trained on a limited number of simulation runs (the "training set") and then replaces the expensive simulation with a fast approximation that can be evaluated in milliseconds or less.
Surrogate models are built through several approaches, each with its own strengths and weaknesses. Polynomial response surfaces fit a low-order polynomial to the training data — simple and interpretable, but limited to smooth, low-dimensional problems. Radial basis functions (RBFs) and Kriging/Gaussian process regression are flexible interpolation methods that provide both a prediction and an estimate of uncertainty — Kriging is particularly popular because the uncertainty estimate guides where to add training points (adaptive sampling). Support vector regression (SVR) uses kernel methods to build nonlinear approximations with good generalization properties. Neural network surrogates — particularly deep networks — are increasingly used for high-dimensional problems where classical methods struggle. Polynomial chaos expansion (PCE) is a spectral method particularly well-suited to uncertainty quantification, expressing the response as a polynomial in the input random variables. Hybrid and multi-fidelity methods combine simulations of different fidelities (e.g., coarse and fine meshes, linear and nonlinear models) to build a surrogate that is both accurate and cheap.
Surrogate models are transforming computational earthquake engineering by making previously infeasible analyses practical. In performance-based earthquake engineering, surrogate models approximate the results of nonlinear response history analysis, enabling probabilistic seismic demand and loss estimation for large building portfolios or for real-time decision support. In probabilistic seismic hazard analysis, surrogates accelerate the computation of hazard curves and deaggregation. In structural reliability, surrogate models enable Monte Carlo and importance sampling analyses that would be impossible with the original simulation. In real-time applications — including earthquake early warning, rapid post-earthquake assessment, and structural control — surrogate models provide the fast predictions needed for decision-making in seconds. In optimization and design, surrogates enable global optimization of structural systems where each evaluation would otherwise take hours. Key challenges include: (1) the curse of dimensionality — most surrogate methods degrade as the number of input variables increases; (2) the trade-off between accuracy and cost — more training data improves accuracy but increases cost; (3) the choice of surrogate type for a given problem; (4) the need for uncertainty quantification in the surrogate itself; and (5) the risk of extrapolation error when the surrogate is evaluated outside its training domain. In Iran, surrogate modeling is increasingly used in performance-based design of important structures, in seismic risk assessment of building portfolios, and in research on real-time monitoring and rapid post-earthquake assessment. The combination of surrogate models with machine learning and physics-informed approaches is an active area of research worldwide.