(193f) Parametric Surrogate Model Generation Using Adaptive Sparse Grid Interpolation

As computational power has continued to increase, complex simulations have become an essential tool for understanding, analyzing, and designing engineered and living systems. Examples of such simulations include systems of ordinary or partial differential equations, finite element models, and agent-based models, and the applications of such models span a wide range of areas such as mechanical and structural design, process modeling, geosciences, systems biology, and many more. As these simulation have become more accurate and complex, the simulations have also become more computationally expensive, potentially taking days per simulation. As a result, it can be very challenging to use complex simulations in frameworks for optimization, control, and uncertainty quantification, especially as the problem size increases. One approach for such applications is to train surrogate models which accurately represent the complex simulation, but are inexpensive to evaluate. Due to the lack of algebraic forms, accurate error estimates can be hard to achieve for a wide range of problems. As a result, there is significant interest in surrogate modeling methods that efficiently search the multidimensional space and converge to a highly accurate model using a limited number of samples.

The presented work tests the performance of a new surrogate modeling algorithm that is based on Smolyak sparse-grids. The algorithm performs adaptive global search of the multidimensional space using a Smolyak grid and the collected samples are used to fit polynomial interpolants as was proposed as part of a recently developed surrogate-based optimization algorithm (Kieslich, Boukouvala, Floudas, JOGO 2018). Rather than searching for a minimum value of a black-box function, the proposed algorithm utilizes an error surrogate based on the difference between interpolants of differing accuracy to predict which regions have the most error compared to the simulation. Numerical integration of the error surrogate is used to approximate the remaining error between the surrogate model and the simulation. The developed algorithm adaptively refines the grid by collecting new points in regions with high predicted error, and convergences when the approximated remaining error is below a selected error tolerance. The algorithm is tested first using a large set of benchmark problems and its performance is compared to existing approaches for surrogate modeling, such as kriging functions and neural networks. Additionally, we will show the performance of the developed method using case studies based on systems of ordinary and partial differential equations.