Active learning for adaptive surrogate model improvement in high-dimensional problems

Area of Science:

• Computational Science and Engineering
• Machine Learning
• Materials Science

Background:

• Surrogate models are crucial for computationally expensive simulations.
• Existing adaptive learning methods struggle with high-dimensional outputs.
• Accurate modeling of complex systems like additive manufacturing is challenging.

Purpose of the Study:

• To develop an efficient approach for constructing and improving surrogate models for high-dimensional input and output problems.
• To address the limitations of current adaptive learning techniques in handling complex, high-dimensional outputs.
• To enhance the accuracy and efficiency of simulations for applications such as additive manufacturing.

Main Methods:

• Identified principal components and features of high-dimensional outputs.
• Applied active subspace technique to find low-dimensional input subspaces for each feature.
• Developed a novel low-dimensional adaptive learning strategy with an exploration-exploitation balance for high-dimensional outputs.
• Mapped new training samples back to the original space for physics model runs.

Main Results:

• Demonstrated the method's effectiveness on a numerical simulation of an additive manufacturing part.
• Successfully modeled high-dimensional residual stress fields with spatial variability.
• Investigated the impact of various adaptive learning parameters on performance.

Conclusions:

• The proposed method efficiently constructs and improves surrogate models for high-dimensional problems.
• The adaptive learning strategy effectively handles high-dimensional outputs by balancing exploration and exploitation.
• This approach offers a significant advancement for simulating complex engineering processes like additive manufacturing.