rq_l¶
L0-R0-(R1,CPE1)
As rq, plus a series inductor L0 for cable and cell inductance, which appears as a tail below the real axis at high frequency.
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 | 34 |
| library defaults | 79.80% | 135 | 317 | 504 | 182 |
| truth x/div 5 | 87.40% | 79 | 214 | 377 | 123 |
| ml guess | 100.00% | 0 | 11 | 33 | 45 |
Circuit.fit()¶
| source of initial parameters | converged | excess med | p90 | p99 | med sweeps |
|---|---|---|---|---|---|
| floor (truth) | 100.00% | 0 | 0 | 0 | 55 |
| library defaults | 90.00% | 160 | 1883 | 16233 | 241 |
| truth x/div 5 | 98.20% | 96 | 330 | 6952 | 161 |
| ml guess | 100.00% | 0 | 11 | 69 | 66 |
Error of the guess¶
Relative error of each guessed parameter before fitting, in %.
L0.l |
R0.r |
R1.r |
CPE1.q |
CPE1.alpha |
|
|---|---|---|---|---|---|
| median | 1.6 | 1.5 | 0.8 | 2.8 | 0.6 |
| p90 | 6.9 | 29.1 | 3.3 | 14.6 | 2.8 |
| p99 | 42.5 | 245.1 | 11.9 | 48.5 | 12.1 |
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, CPE exponents ±0.15.
- 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.