sei_randles_wo¶
R0-(R1,CPE1)-(R2-Wo2,CPE2)
As sei_randles, with a finite-length open Warburg element instead of semi-infinite, for diffusion into a layer with a blocking boundary like an intercalation particle. The 45° diffusion tail turns vertical at low frequency.
ML model: 270k parameter 1D CNN, trained on synthetic data, 2.5 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 | 276 |
| library defaults | 23.20% | 322 | 1504 | 7004 | 676 |
| truth x/div 5 | 26.00% | 192 | 730 | 5683 | 401 |
| ml guess | 91.30% | 16 | 252 | 5904 | 257 |
Circuit.fit()¶
| source of initial parameters | converged | excess med | p90 | p99 | med sweeps |
|---|---|---|---|---|---|
| floor (truth) | 100.00% | 0 | 0 | 0 | 397 |
| library defaults | 41.40% | 928 | 43062 | 140937 | 4856 |
| truth x/div 5 | 52.60% | 746 | 17284 | 54826 | 3144 |
| ml guess | 91.00% | 19 | 1094 | 38252 | 414 |
Error of the guess¶
Relative error of each guessed parameter before fitting, in %.
R0.r |
R1.r |
CPE1.q |
CPE1.alpha |
R2.r |
Wo2.z0 |
Wo2.tau |
CPE2.q |
CPE2.alpha |
|
|---|---|---|---|---|---|---|---|---|---|
| median | 0.6 | 1.7 | 3.2 | 0.6 | 23.2 | 46.9 | 49.0 | 5.6 | 1.2 |
| p90 | 4.8 | 11.9 | 20.4 | 4.1 | 84.2 | 255.1 | 306.0 | 43.9 | 11.6 |
| p99 | 63.9 | 50.1 | 97.2 | 16.0 | 250.3 | 1419.4 | 5491.2 | 226.0 | 32.2 |
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.