Active learning for efficiently training emulators of computationally expensive mathematical models.

Area of Science:

• Computational Science
• Statistical Modeling
• Applied Mathematics

Background:

• Emulators are fast statistical approximations of computationally expensive simulators, crucial for tasks like sensitivity analysis and model calibration.
• Developing accurate emulators typically requires numerous simulator evaluations, leading to significant computational expense.
• Efficient emulator development is vital for accelerating scientific research and decision-making processes.

Purpose of the Study:

• To introduce a novel self-terminating active learning algorithm for efficient emulator development.
• To compare the performance of the proposed algorithm against geometric sampling and other active learning methods.
• To evaluate emulator accuracy using root mean square error (RMSE) and maximum absolute deviation (MAX).

Main Methods:

• A self-terminating active learning algorithm was developed to optimize emulator construction.
• The proposed algorithm was compared with random latin hypercube sampling, maximum projection designs, and treed Gaussian Processes.
• Performance was evaluated on seven benchmark functions and a prostate cancer screening model.

Main Results:

• Active learning algorithms yielded emulators with lower RMSE and MAX in simulators with spatially varying smoothness.
• The proposed algorithm demonstrated satisfactory performance across all tested scenarios.
• The new algorithm exhibited lower variability and comparable or superior performance to treed Gaussian Processes in most cases.

Conclusions:

• The proposed self-terminating active learning algorithm efficiently develops accurate emulators, reducing computational costs.
• This method is particularly effective for simulators with complex, non-uniform input domain characteristics.
• The algorithm offers a robust and reliable alternative for emulator development in scientific modeling.