Dimensionality Reduction in Surrogate Modeling: A Review of Combined Methods.

Area of Science:

• Engineering
• Computational Science
• Data Science

Background:

• Surrogate modeling is crucial for complex engineering simulations, but high dimensionality leads to computational challenges.
• The curse of dimensionality increases modeling demand and resource consumption in engineering processes.
• Nonlinear phenomena in high-complexity processes exacerbate execution and memory demands.

Purpose of the Study:

• To review current literature on integrating dimensionality reduction with surrogate modeling methods.
• To discuss the mathematical implications, applications, and limitations of these combined techniques.
• To identify avenues for future research in this interdisciplinary area.

Main Methods:

• Literature review of state-of-the-art dimensionality reduction algorithms.
• Literature review of advanced surrogate modeling techniques.
• Analysis of studies combining dimensionality reduction and surrogate modeling.

Main Results:

• Dimensionality reduction simplifies surrogate models for high-dimensional problems.
• Reduced computation is achieved while retaining sufficient process representation accuracy.
• Current research combines these methods to mitigate computational complexity.

Conclusions:

• Integrating dimensionality reduction with surrogate modeling offers a viable solution to computational challenges in complex engineering.
• Further research is needed to fully explore the potential and limitations of these combined approaches.
• This integration is key to efficient and accurate modeling of high-dimensional engineering processes.