How many simulations are performed in adjoint calculations?#
Date |
Category |
|---|---|
2023-12-21 21:14:12 |
Inverse Design |
At least two simulations, the forward and the adjoint one, are performed when running inverse design optimizations using the adjoint plugin.
However, for broadband simulations, more than one adjoint simulation may be necessary depending on the type and number of monitors used.
Single-frequency differentiation
If all monitors are set to differentiate at a single frequency, only one adjoint simulation is needed per forward simulation, regardless of how many monitors are present. This works because adjoint sources can be linearly combined.Monitors with well-defined field profiles (e.g., ModeMonitor or DiffractionMonitor)
Single monitor: One adjoint simulation per forward simulation is sufficient, even for broadband frequencies.
Multiple broadband monitors: Multiple adjoint simulations may be needed. The plugin automatically selects the most efficient strategy:
Group single-frequency monitors into one adjoint simulation, or
Run one adjoint simulation per monitor that includes all frequencies.
Monitors with arbitrary field profiles (e.g., FieldMonitor)
These do not support broadband adjoint sources, so one adjoint simulation is needed per frequency.
If multiple field monitors share the same frequency, they can be grouped into a single adjoint simulation.
Below is a summary of how the number of adjoint simulations depends on monitor type, frequency usage, and monitor count:
| Monitor Type | Frequencies | # of Monitors | # of Adjoint Simulations | ||||—| | Any | Single | Any | 1 per forward simulation | | Mode / Diffraction | Multiple | 1 | 1 per forward simulation | | Mode / Diffraction | Multiple | >1 | Depends (≤ #monitors or ≤ #frequencies) | | Field (arbitrary) | Single | Any (same freq) | 1 | | Field (arbitrary) | Multiple | 1 | = # of frequencies | | Field (arbitrary) | Multiple | >1 (mixed freqs) | = # of unique frequencies |
We highly recommend watching the Inverse Design lectures if you are new to the adjoint method. You can also go through this tutorial for an introduction to the basic concepts related to automatic differentiation and adjoint optimization.