Adjoint Optimization using Minimax

[satadrudas]

Hi,
Once again, thanks to all the people who are maintaining MEEP. Great work!

I was trying out optimizing a 3dB directional coupler (DC) using the code reference from the Adjoint tutorial and stumbled upon few things when optimizing the DC.

1. In point number 5 of the Adjoint tutorial , it says that the damping is done for beta<50 however in the code the damping is done for all beta values, would that affect the final design?

2. In point number 1 of Adjoint tutorial , it is mentioned that before the final epoch, the design must be binarized with a large beta value, how I don't see any part of the code which does that, ...or is the beta= 128 of the final epoch sufficient for that binarization?

3. In point 6 of the tuotrial, it is mentioned "When subpixel smoothing is enabled (do_averaging=True), the weights are projected internally using the beta parameter. For this reason, any preprocessing (i.e., mapping) of the weights outside of the MaterialGrid should apply only a filter to the weights but must not perform any projection." Can we do it keeping the internal beta(in the MeterialGrid )=0 and do external projection via mapping function?

4. For the DC optimization, other than the geometry, most of the code structure is similar to that of the tutorial except for the the betas and the max_evals, which I just increased the max_evals for the last 2 betas to 50. The resolution is 20. The objective function is based on Phase-injected topology optimization as suggested to me by @smartalecH. However the my final design is still not much binarized
   EDIT: For now I am running the optimization with more number of evaluations in the last epoch. Will update once its done.

If my understanding is right then the last iteration, the epivar value id or the minimum lengthscale and hence it shot up, but about the binarization, is this behaviour expected?

Any suggestions to improve?

Thanks

[satadrudas]

However, with the sub-pixel smoothing being active throughout and not just fo the later epochs and no damping, I get a binary design with beta=128 (though heavily under performing one) which is expected since the glc() function in the Adjoint tutorial enforces binarizaion. But why is it not the case when there is damping and subpixel smothing???

[satadrudas]

So, I have ran an adjoint optimization with sub-pixel smoothing throughout all epochs and no damping. the betas and number of evaluations are as follows, betas = [8, 16, 32, 64, 128], max_evals = [20, 20, 20, 20, 50] and instead of the part where we give beta=0 in the mapping function and given in the MaterialGrid, I have just given beta in the mapping function itself and keeping beta=0 in the MaterialGrid. While I did get a proper binary design in the end, but the performance deteriorates in the last epoch as expected from minimum length contraints function glc()

Perhaps I'll have to binarize the weights before the last epoch, which I am going to do now. Is this the right approach? Any other inputs from you guys would be very helpful.

[satadrudas]

So now that I ran an adjoint optimization with: betas = [8, 16, 32, 64, 128, 256]
max_evals = [30, 30, 30, 60, 60, 100] (basically increased the maxevals of the last few epochs), I seem to get a better design. Made a small correction to the objective function and with increased number of iterations per epoch did the job for me.