Inverse design

Backend lightsmith-inverse (method inverse, package lightsmith.inverse). Density-based topology optimisation of optimization problems. It needs PyTorch (the gpu extra), and runs on the CPU or a GPU.

3D inverse design

Another branch is adding 3D inverse design. See 3D inverse design.

Method

• Backends. The optimiser works with any backend that is differentiable and implements differentiable_solve. In 0.1 that is lightsmith-fdfd (2D), the default.
• Density pipeline. For each design region:
• raw density ρ ∈ [0, 1];
• mirror symmetry;
• normalised conic filter;
• tanh projection (β, η);
• ε = ε_low + ρ·(ε_high − ε_low).
• Minimum feature size. Imposed with the geometric constraints of Zhou et al. (2015), in the form of Hammond et al. (2021). They switch on once β reaches lengthscale_from_beta.
• β continuation. β is multiplied by beta_growth every beta_every iterations, up to beta_max.
• Optimisers.
• mma: globally convergent MMA (Svanberg 2002); the objective never increases.
• adam: Adam, projected onto the box.
• lbfgsb: SciPy L-BFGS-B.
• Final design.
• Thresholded; objective_binary is its score.
• Contoured with marching squares.
• Exported as prism structures and re-solved for validation.

Settings

The spec fields are listed on Inverse design (problem kind). OptimizerSettings defaults:

Setting	Default
method	"mma"
max_iter	100
learning_rate (Adam)	0.02
move_limit (MMA)	0.2
beta_start, beta_max, beta_growth, beta_every	4, 64, 2, 20
lengthscale_weight, lengthscale_from_beta	100, 16
ftol	0: stop when the relative improvement over 10 iterations falls below this

Export (lightsmith.inverse.export, no extra dependencies):

• marching_squares, which returns contours with their nesting depth;
• to_structures;
• write_gds, a built-in GDSII writer. Holes go to datatype + 1, to be subtracted downstream;
• to_gdsfactory, which needs the layout extra and subtracts the holes itself.

Checkpoints. inverse.optimize(..., checkpoint="run.npz") saves progress periodically and resumes from the file when it is run again.

Validation

All tests are in tests/test_inverse.py and need PyTorch.

Test	Check	Tolerance
test_filter_and_projection	the filter preserves constants; the projection is monotone	1e-12
test_lengthscale_constraint_flags_thin_features	a 20 nm line is penalised far more than a 200 nm line	> 100×
test_mma_is_monotone_on_a_quadratic	monotone decrease within the bounds	1e-12
test_marching_squares_disc_and_ring	disc area against πr²; re-rasterised ring	2 %; > 98 % of pixels
test_gds_roundtrip	written polygons read back	1 nm
test_bend_topology_optimisation_improves_monotonically: 2D Si 90° bend, 12 MMA iterations	objective rises from < 0.1 to > 0.8; binary design > 0.6; exported polygons agree with the binary score	within 0.15
test_checkpoint_resume_and_beta_continuation	a resumed run reproduces the history	exact
test_field_objective_and_lbfgsb	a field objective improves	—

Limits

• 2D in 0.1: the filters and the region mapping are 2D, and FDFD is 2D.
• Design regions must stay at least 3 cells from every port plane, and span at least 2 grid cells.
• Warns when the final design is less than 90 % binary (raise beta_max or max_iter). Warnings from the validation solve are passed on with the prefix validation:.