Global Optimization Employing Gaussian Process-Based Bayesian Surrogates.

Area of Science:

• Computational Physics
• Applied Mathematics
• Machine Learning

Background:

• Complex physics simulations demand significant computational resources, necessitating efficient parameter optimization.
• Global optimization techniques are crucial for identifying optimal input parameters from existing simulation data.
• Bayesian frameworks offer a probabilistic approach to model complex systems.

Purpose of the Study:

• To develop an efficient global optimization strategy for expensive physics simulations.
• To leverage Gaussian processes for creating accurate surrogate models of complex functions.
• To minimize computational cost while maximizing the discovery of optimal parameters.

Main Methods:

• Utilized Gaussian processes within a Bayesian framework to build self-consistent surrogate models.
• Employed expectation values of hyperparameters for computational efficiency.
• Alternated between expected improvement and maximum variance utility functions to guide parameter selection.
• Iteratively updated the surrogate model with new data points until convergence.

Main Results:

• Demonstrated proof of principle for the proposed global optimization method using mock data in one and two dimensions.
• The surrogate model effectively guided the search towards the extremum of the underlying function.
• Alternating utility functions mitigated the limitations of individual approaches.

Conclusions:

• The proposed Bayesian global optimization approach offers an efficient strategy for parameter exploration in computationally intensive simulations.
• Gaussian process surrogate models, combined with adaptive utility functions, can significantly reduce the number of required simulations.
• This method provides a viable solution for accelerating scientific discovery in fields reliant on complex modeling.