Choosing hyperperameters for minimum feature size constraint functions for Adjoint Optimization

[satadrudas]

Hi,

I was going through the Adjoint Solver tutorial with minimum feature size in the MEEP documentation. Can someone please explain to me what does the parameters a1, b1 and c0 represent?

From the paper Minimum length scale in topology optimization by geometric constraints, I got to know that c0 is the decay rate of the Indicator functions. c0 is used as an argument for constraint_void() and constraint_solid() in the glc() function. In the source code of constraint_void() and constraint_solid() it is mentioned that the the c0 value lies withing the range (1e0 - 1e8). However, in the tutorial, c0 = 1e7 * (filter_radius * 1 / resolution) ** 4 which is equal to 0.0008100000000000001 since filter_radius = 0.15 and resolution = 50.

So why is the value of c0 not in the range (1e0 - 1e8) as mentioned in the source code?

Also in the paper Phase-InjectedTopologyOptimizationfor ScalableandInterferometricallyRobustPhotonicIntegratedCircuits, c=8500. How do we choose a good value for c0 ? Trial and error ?

[smartalecH]

Trial and error, like most TO hyperparameters.

Not super helpful, I know. But like machine learning, there's a lot of art to this. But unlike machine learning, there isn't enough investment in the tooling or methods to better democratize the process (or better yet, automate it altogether).

I typically do quite a bit of hyperparameter optimization for each design problem.

[satadrudas]

Hi, thanks for your answer.

Also, I did understand the purpose of c0, but could you also please teel me the role of a1 and b1 for completeness?