Active Manifold and Model Order Reduction to Accelerate Multidisciplinary Analysis and Optimization - presented by Prof. Charbel Farhat

Active Manifold and Model Order Reduction to Accelerate Multidisciplinary Analysis and Optimization

Prof. Charbel Farhat

Prof. Charbel Farhat
Slide at 1:00:31
Charbel Conclusions PMOR is data-driven, physics-based machine learning for surrogate modeling it is more versatile than purely data-driven regression-based learning it is more resilient to data dependency and overfitting it performs better when faced with conditions outside the training bounds it is interpretable because it learns from both models and data it seems complex however, but primarily due to the lack of publicly available software Training cost is affected by curse of dimensionality, regardless of type of learning employed for higher-dimensional parameter domains D, adaptive training is necessary for MDAO greedy procedure is a popular adaptive sampling procedure that alleviates the impact of the curse of dimensionality but does not completely mitigate it on its own Active manifold is a technique that attempts to identify and exploit the underlying low- dimensional structure of high-dimensional data mitigates the curse of dimensionality by focusing the training on DAM C D accelerates the solution of realistic MDAO problems by orders of mangnitude in its form developed so far, it guarantees a faster local optimum
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Summary (AI generated)

PR is a data-driven physics-based machine learning method that is more versatile than data-driven regression. It is resilient to data dependency and overfitting due to the physics it incorporates, making it perform better in conditions outside of the training bounds. It is also interpretable because it learns from both models and data. However, it may seem complex as publicly available software for model reduction is not readily accessible like other machine learning tools.

In research, popularity is not a concern. Training costs are affected by the curse of dimensionality, especially in higher-dimensional parameter spaces. Adaptive training, such as the greedy procedure, can help alleviate this issue but may not fully mitigate it. An Active manifold can be used to learn the mathematical structure of the problem and accelerate the solution of MDAO problems by identifying appropriate regions for problem-solving. This approach has shown significant acceleration in solving realistic MDAO problems.

One downside of the Active manifold approach is that it currently only works with local optimization, which may require additional effort to reformulate in certain contexts.