sei_randles¶
R0-(R1,CPE1)-(R2-W2,CPE2)
A randles circuit with an additional RQ element, often attributed to a solid electrolyte interphase (SEI) or other surface film.
ML model: 270k parameter 1D CNN, trained on synthetic data, 2.3 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 | 103 |
| library defaults | 30.40% | 400 | 1180 | 5233 | 726 |
| truth x/div 5 | 41.60% | 228 | 672 | 2386 | 416 |
| ml guess | 99.10% | 0 | 52 | 334 | 103 |
Circuit.fit()¶
| source of initial parameters | converged | excess med | p90 | p99 | med sweeps |
|---|---|---|---|---|---|
| floor (truth) | 100.00% | 0 | 0 | 0 | 148 |
| library defaults | 53.60% | 692 | 16594 | 80818 | 2018 |
| truth x/div 5 | 66.10% | 554 | 5597 | 37704 | 1148 |
| ml guess | 99.00% | 0 | 66 | 1797 | 147 |
Error of the guess¶
Relative error of each guessed parameter before fitting, in %.
R0.r |
R1.r |
CPE1.q |
CPE1.alpha |
R2.r |
W2.aw |
CPE2.q |
CPE2.alpha |
|
|---|---|---|---|---|---|---|---|---|
| median | 1.3 | 2.5 | 4.7 | 0.9 | 8.1 | 5.7 | 10.6 | 3.4 |
| p90 | 4.7 | 15.6 | 23.9 | 4.7 | 42.9 | 41.6 | 58.6 | 16.2 |
| p99 | 58.1 | 66.7 | 71.1 | 14.1 | 149.4 | 171.9 | 194.2 | 36.9 |
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.