Surrogate-Based Optimization in Engineering Design

Surrogate-based optimization has emerged as a cornerstone methodology for tackling expensive engineering design problems by replacing costly high-fidelity simulations or physical experiments with computationally efficient approximations. These surrogate models, also known as metamodels, capture the essential behaviour of complex objective functions and constraints, enabling iterative exploration and exploitation of large design spaces. Common surrogate formulations include Gaussian process regression (kriging), radial basis functions, polynomial approximations and neural network-based emulators. Central to this framework is the use of an acquisition function that balances sampling in regions of high uncertainty against exploitation of promising designs. Extensions to multi-objective, constrained and multi-fidelity settings allow simultaneous consideration of several performance metrics and levels of model detail. Surrogate-based strategies have been successfully applied across aerospace airfoil design, automotive crashworthiness, structural optimisation, energy-efficient building systems and advanced materials development. By dramatically reducing the number of expensive function evaluations, these methods accelerate innovation, lower computational cost and support sustainable engineering practices on a global scale.

Research from Nature Portfolio

Recent studies have extended surrogate-based optimization to mixed-variable engineering design by integrating a latent-variable approach within a Bayesian framework. Qualitative factors such as material type or morphology are mapped to continuous latent coordinates, which are then incorporated into a Gaussian process surrogate. This methodology captures complex correlations between categorical and numerical variables more accurately than traditional dummy-coding schemes. Demonstrations on mixed-variable materials design problems—including optimisation of light-absorbing microstructures in quasi-random solar cells and combinatorial searches for perovskite compositions—have shown enhanced predictive accuracy and intuitive visualisation of qualitative factor effects. The approach is generic and can be applied to any expensive simulation involving mixed design variables.

Surrogate-Based Optimization in Engineering Design publication trend

The graph below shows the total number of articles in surrogate-based optimization in engineering design across all publications each year (not limited to Nature Index journals).

Technical terms

Surrogate model: an approximate mathematical representation of a high-fidelity simulation or experiment, used to predict performance metrics with lower computational cost.

Gaussian process (Kriging): a statistical technique that constructs a smooth probabilistic model of a function based on observed data, providing estimates of uncertainty.

Bayesian optimisation: an iterative strategy that uses a probabilistic surrogate and an acquisition function to select the most informative points for evaluating expensive black-box functions.

Acquisition function: a mathematical criterion used within Bayesian optimisation to balance exploration of uncertain regions and exploitation of promising areas in the design space.

Adaptive sampling: a dynamic process of selecting new evaluation points based on current surrogate model performance to improve approximation quality efficiently.

Latent-variable model: an approach that maps qualitative design variables into a continuous numerical space to enable their integration within Gaussian process surrogates.

References

1. Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables. Scientific Reports (2020).
2. State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging. Archives of Computational Methods in Engineering (2020).
3. Boosting Data-Driven Evolutionary Algorithm With Localized Data Generation. IEEE Transactions on Evolutionary Computation (2020).
4. High-dimensional Bayesian optimization using low-dimensional feature spaces. Machine Learning (2020).