Application and comparison of several adaptive sampling algorithms in reduced order modeling.

Area of Science:

• Computational Science and Engineering
• Numerical Analysis
• Model Order Reduction (MOR)

Background:

• Model Order Reduction (MOR) is vital for simulating complex systems in science and engineering, including nuclear reactor analysis and fluid mechanics.
• The effectiveness of Reduced Order Models (ROMs) hinges on the offline stage's basis function selection, which is critically dependent on parameter space sampling.
• Traditional sampling strategies often struggle with complex parameter spaces, posing a significant challenge in MOR.

Purpose of the Study:

• To systematically assess and compare the performance of three prevalent adaptive sampling algorithms within the context of Model Order Reduction.
• To investigate the application and effectiveness of pseudo-gradient sampling, adaptive sparse grid sampling, and adaptive training set extension for MOR.
• To demonstrate the practical utility of these adaptive sampling techniques in real-world engineering problems, such as nuclear reactor core simulations.

Main Methods:

• Focus on three adaptive sampling algorithms: pseudo-gradient sampling, adaptive sparse grid sampling, and adaptive training set extension.
• Systematic performance assessment and comparison against standard sampling strategies.
• Application and validation in diverse scenarios, including nuclear reactor cores and convection problems.

Main Results:

• Adaptive sampling algorithms demonstrate superior performance in capturing divergent and oscillating regions of the parameter space compared to standard methods.
• Pseudo-gradient sampling proves effective for small-scale MOR problems.
• Adaptive sparse grid sampling and adaptive training set extension are well-suited for large-scale sampling challenges in MOR.

Conclusions:

• Adaptive sampling algorithms represent a significant advancement in building effective Reduced Order Models (ROMs).
• These algorithms enhance sampling efficiency and accuracy, particularly in complex and challenging parameter spaces.
• The validated applications confirm the practical value of adaptive sampling in critical engineering fields like nuclear reactor analysis.