Towards the optimal design of numerical experiments.

Area of Science:

• Computational Science
• Machine Learning
• Numerical Analysis

Background:

• Nonlinear surrogate models are crucial for complex simulations.
• Optimal experimental design is key to efficiently constructing accurate surrogate models.
• Existing methods may not optimally leverage model divergence for design.

Purpose of the Study:

• To introduce and evaluate a novel method for optimal numerical experiment design.
• To improve the accuracy and efficiency of nonlinear surrogate model construction.
• To compare the proposed method against established experimental design techniques.

Main Methods:

• Developed the Learner Disagreement from Experiment Resampling (LDR) method.
• Utilized active learning and resampling techniques for iterative design.
• Applied LDR to neural network models with bootstrap resampling.
• Tested LDR on orthogonal polynomial models with leave-one-out resampling.

Main Results:

• LDR effectively guides the selection of numerical experiments for improved surrogate model accuracy.
• The method demonstrates competitive or superior performance compared to random and D-optimal selection.
• Divergence analysis of model predictions is a powerful tool for experimental design.

Conclusions:

• The LDR method offers an effective strategy for optimal experimental design in surrogate modeling.
• Iterative refinement based on model disagreement enhances predictive accuracy.
• LDR provides a valuable alternative for constructing accurate nonlinear surrogate models.