Corrosion prediction across publications

1 Introduction

Pitting corrosion is local breakdown of a passive metal: protection fails on a small area of the surface and a stable corrosion pit can grow there. For passivating alloys a key indicator is the pitting potential, $E_{\text{pit}}$: under the same protocol, a higher value usually means stable local breakdown begins at a higher potential. $E_{\text{pit}}$ depends not only on composition but on solution chemistry, chloride concentration, pH, temperature, microstructure, surface state and polarization regime; potentials measured against different reference electrodes must be brought to one scale.

Multi-principal-element alloys span a very large composition space, and their corrosion depends on composition, phases, processing and environment. Chromium matters for passivation, but Cr content alone does not predict pitting resistance. Testing every composition experimentally is impractical, so published electrochemical data are attractive for pre-screening. Machine learning has been applied to MPEA corrosion before, but materials models can lose much of their accuracy on data from another distribution, and corrosion transfer is especially hard because publications differ in environment, material state and protocol.

Question. How reproducibly can $E_{\text{pit}}$ of MPEAs be predicted from literature data on composition and test conditions, and does the reliability estimate hold on publications the model has not seen?

Hypothesis. Restricting the task chemically and rejecting predictions with high expected error lowers the MAE of accepted predictions and keeps that advantage on unseen publications.

2 Materials and methods

2.1 Data

The main source is the open MPEA corrosion database of Birbilis et al.: 619 records, 610 after cleaning, with 583 values of $i_{\text{corr}}$, 607 of $E_{\text{corr}}$ and 328 of $E_{\text{pit}}$. The main task kept records with a known $E_{\text{pit}}$, chromium in the composition, a stated solution concentration and a neutral chloride environment: 232 measurements from 54 publications. Potentials were converted to volts versus the saturated calomel electrode where the source allowed an unambiguous conversion; missing pH, temperature or surface state stayed unknown.

For the external test, the Nyby dataset and the additively manufactured MPEA database were used. After removing overlaps and ambiguous duplicates, set C1 held 40 measurements from 12 publications (39 AM-MPEA, one Nyby). None of it was used in training, and because AM-MPEA dominates, C1 mainly tests transfer to that one source.

A descriptive NaCl subset (202 Cr-containing measurements, 52 sources) shows why the problem is hard: the rank correlation between Cr content and $E_{\text{pit}}$ is close to zero (ρ = +0.03), the number of alloying elements shows no clear trend (ρ = 0.07), and 181 of 202 measurements were taken in 0.6 M NaCl. These one-dimensional relations are not causal.

2.2 Features and model

Composition is given as 24 atomic fractions, plus the number of components and the ideal configurational entropy $S_{\text{mix}}/R = -\sum_i x_i \ln x_i$. The model also gets electrolyte concentration, a normalized environment label and available processing features. Phase composition and post-test characterization were excluded, since they are unknown for a new alloy before synthesis.

In each training split the procedure compared random forest, extremely randomized trees, gradient boosting, ridge regression and model averaging, choosing only on training publications. For every query it produced a prediction $\hat E_{\text{pit}}$ and an expected absolute error $\hat e$, computed only from information available before the true value is known: composition distance to the training data, disagreement and spread among models, the number of nearby literature examples, and training $E_{\text{pit}}$ statistics. A threshold on $\hat e$, set inside the training split, decides whether a numeric prediction is returned; the share returned is the coverage.

2.3 Validation

Internal validation used 30 repeated splits by whole publication: a publication is entirely in training or entirely in test, and model choice, features, normalization and the rejection threshold are fitted on training data only. A random row split served only as a reference. The frozen model and rule were then applied once, without tuning, to the pre-specified external set C1. Only after that result was fixed were external data added to development: an expanded base of 594 measurements from 97 publications (232 internal, 323 Nyby, 39 AM-MPEA), which from then on is not an independent test.

Two further analyses used the expanded base: local calibration, where a fully held-out publication stands in for a new lab and $k$ = 1, 2, 3, 5, 10 or 20 of its measurements correct a systematic offset; and candidate selection, where small changes of measured compositions (2 at.% moved between elements already present, at a fixed 0.6 M NaCl) are kept only if they pass the expected-error threshold and have support from at least three nearby publications.

3 Results

3.1 Internal validation

Across 30 publication splits, the median MAE of all predictions was 0.255 V with median R² = 0.244. In the 28 splits where the rule accepted at least some queries, MAE fell from 0.249 V for all predictions to 0.171 V for accepted ones, with 61.8% of queries accepted; the error dropped in 26 of 28 splits. The Spearman correlation between expected and actual absolute error was 0.407.

3.2 External test

On C1 the MAE was 0.281 V and R² = −0.676: worse than predicting the external set's own mean. The rule accepted 23 of 40 queries (57.5%), but their MAE rose to 0.324 V, and expected and actual errors were barely related (ρ = 0.071). The selection that worked inside the source base did not find a more accurate group on new publications. Composition and concentration do not describe the whole experiment: microstructure, surface preparation, pH, temperature and polarization may all differ between publications, and these data cannot say which mattered most.

3.3 After adding the external data

On the expanded 594-row base, 30 new publication splits gave median MAE 0.238 V and median R² = 0.180, and the rule lowered mean MAE from 0.238 to 0.192 V at 46.6% coverage. Because the external data were already used in development, this is not a new independent test.

3.4 Local calibration

A few measurements from the new "lab" corrected much of the offset:

With 20 measurements only three publications qualified, so that point is unstable. This is a retrospective simulation on publications, not yet tried in a real new laboratory.

3.5 Candidates for the next experiment

From the measured parent compositions, 1,684 nearby variants were generated; 1,041 passed the expected-error threshold, 521 had support from at least three nearby publications, and 354 met both. Five were chosen for diversity of parents and literature regions, not ranked by predicted $E_{\text{pit}}$:

#	Composition, at.%	Predicted $E_{\text{pit}}$, V	Expected error, V	Supporting publications
1	Al0.07Co24.01Cr22.66Fe24.85Mn0.51Ni27.90	0.310	0.213	16
2	Co22Cr20Fe20Ni20W18	0.286	0.256	3
3	Co19.61Cr21.61Fe17.61Mn19.61Nb1.96Ni19.61	0.197	0.120	6
4	Co22Cr20Fe20Mn18Ni20	0.175	0.101	6
5	Al15.33Co16.67Cr16.67Fe16.67Ni16.67Ti18	0.185	0.268	4

After the unfavourable external test, none of them can be considered confirmed without a new standardized measurement.

4 Discussion

The method could apply to other corrosion targets and new lab data, but the strict quantitative check here covers only $E_{\text{pit}}$ of Cr-containing alloys in chloride solutions. Inside the source base the expected-error estimate picked out more accurate predictions; on the external set the accepted share was less accurate than all queries. A reliability rule therefore needs checking on new sources just like the model itself.

The weak external result is consistent with the available features not fully describing the chemical and experimental context: environment chemistry, the passive film, microstructure, surface preparation, polarization regime and the reference electrode can all change between publications at once. New measurements should systematically record pH, temperature, surface preparation, reference electrode, scan rate, hold time, microstructure and material state.

Earlier MPEA corrosion work studied environmental and physico-chemical descriptors, physics-guided composition selection, and supervised learning with generative data augmentation. In the available description of the last of these we found no splitting of whole publications between training and test, so its metrics cannot be compared directly with this external setting.

Limits. Literature records often omit pH, temperature, scan rate, surface state, reference electrode and microstructure. The internal set has 232 measurements from 54 publications and the external set 40 from 12, 39 of them AM-MPEA. No independent test followed the expansion to 594 rows. A publication only approximates a laboratory, and the five compositions have not been synthesized or measured. The next step is a series of in-house measurements under one pre-specified protocol.

5 Conclusion

A reproducible way to assess the reliability of ML predictions of $E_{\text{pit}}$ from literature data was built and tested on Cr-containing alloys in chloride solutions (232 measurements, 54 publications). Internally, the MAE of accepted predictions fell from 0.249 to 0.171 V. On the pre-specified external set the rejection rule did not transfer: MAE rose from 0.281 to 0.324 V. The literature base holds a useful internal signal, but transfer to a new experimental context remains unreliable. The approach can support pre-screening and experiment planning, not replace experimental testing.

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