two_rc¶
R0-(R1,C1)-(R2,C2)
A series resistance R0 and two RC elements, giving two ideal semicircles. Used when two processes have well separated time constants, for example a surface film and charge transfer.
ML model: 69k parameter 1D CNN, trained on synthetic data, 1.6 ms per guess. See Training.
Benchmarks¶
Plain LM¶
| source of initial parameters | converged | excess med | p90 | p99 | med sweeps |
|---|---|---|---|---|---|
| floor (truth) | 100.00% | 0 | 0 | 0 | 44 |
| library defaults | 67.40% | 168 | 374 | 1025 | 182 |
| truth x/div 5 | 75.50% | 79 | 215 | 475 | 124 |
| ml guess | 100.00% | 0 | 11 | 22 | 45 |
Circuit.fit()¶
| source of initial parameters | converged | excess med | p90 | p99 | med sweeps |
|---|---|---|---|---|---|
| floor (truth) | 100.00% | 0 | 0 | 0 | 65 |
| library defaults | 91.60% | 176 | 702 | 5782 | 258 |
| truth x/div 5 | 92.80% | 125 | 712 | 4519 | 207 |
| ml guess | 100.00% | 0 | 11 | 22 | 66 |
Error of the guess¶
Relative error of each guessed parameter before fitting, in %.
R0.r |
R1.r |
C1.c |
R2.r |
C2.c |
|
|---|---|---|---|---|---|
| median | 0.4 | 0.7 | 0.9 | 1.3 | 2.4 |
| p90 | 1.8 | 2.3 | 4.0 | 10.5 | 16.0 |
| p99 | 26.7 | 5.8 | 10.8 | 57.6 | 46.1 |
Benchmark notes¶
Synthetic benchmarks use 1000 spectra drawn from the same distribution as the training data, with a different seed: 4 to 8 decade sweeps of 20 to 100 points, with 0.2% to 5% noise.
- floor (truth): start from the true parameters.
- library defaults: start from the
Circuit()placeholder values. - truth x/div 5: true magnitudes multiplied or divided by 5 at random.
- ml guess: start from
Circuit.guess().
Plain LM is a single-start Levenberg-Marquardt. Circuit.fit() is LM that also screens candidate starts and restarts on bad fits.
Converged: final cost within 1% of the fit from the truth. Sweeps: impedance evaluations of the whole spectrum, including Jacobians. Excess: sweeps beyond the fit from the truth, for converged fits only.