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Inquiry about general algorithm for sensitivity analysis
Posted 2024年9月18日 GMT-4 05:20 Optimization, Studies & Solvers Version 5.5 1 Reply
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Hello, I have a question about sensitivity analysis in Comsol. This is not a specific question about a specific simulation problem, but a general question about the calculation algorithm of the calculator embedded in the software.
If you read the introduction in the "Theory for the sensitivity interface" section of the reference manual for Comsol 5.5, it says that it is possible to calculate sensitivity for any objective function. It is surprising that sensitivity calculation is possible for "any objective function." I wonder how this is possible. Since Comsol is a physics simulation software, I thought that it is possible to calculate sensitivity only for objective functions that have physical meaning. Please explain this. Also, if there is a related paper, please recommend it.
In addition, even when the objective function is a physical scalar quantity, the calculation of terms such as round(Q)/round(u), round(L)/round(zeta), which are partial derivatives with respect to the design variables, seem to be determined by the objective function, the governing equation of the physical phenomenon L, and the design variable zeta. Since these are parts that are arbitrarily set by the user, I wonder if it is impossible to calculate them using general algorithms. I am curious about how general algorithms can be used for these calculations. Please explain this. Also, if there is a related paper, please recommend it.
Thank you in advance.
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Limiting support to objectives with "physical meaning" only makes sense for software where there are separate hard coded sensitivity computations for each objective, similar to how some "multiphysics" software only support certain multiphysics couplings, but that is not how COMSOL works.
COMSOL relies on symbolic differentation of the equation systems at a high level, so the code is the same regardless of the coupling/objective. It is this technology that allows custom multiphysics couplings and support for arbitrary objective functions.
Best regards,
Kristian E. Jensen
Technical Product Manager, Optimization