1. The short version / before you start / where this fits in the series

• MI is a tool for narrowing where to look. The number of possible alloy compositions is huge: mixing just five elements in 1 at.% steps gives about 4.6 million compositions, and eight elements give about 26 billion Our calculation. We cannot try them all, so a function that "learns trends from past data" is used to narrow down the next candidates.
• Some cases were verified by experiment, but they are few, and we found no independent replication. In a search for shape memory alloys, 36 compositions out of a space of about 800,000 were made, and 14 had a smaller thermal hysteresis than any in the original data Sourced [Reference 8]. There are also reports of making and measuring proposed alloys for a nickel-base superalloy, a cast aluminium alloy and a TWIP steel [References 6, 9, 10].
• "R² = 0.98" does not mean "unseen steel grades are predicted too". R² of 0.90 to 0.98 was reported for fatigue strength of steel, but under leave-one-out cross-validation (LOOCV), in which one record is held out at a time Sourced [Reference 2]. In synthetic data, R² was 0.98 with a random split and -0.31 (median) when a whole grade was held out Our calculation.

2. Why alloys suit MI, and why they are hard

(1) Why they suit it: many combinations, and continuously adjustable composition

An alloy is a material whose composition can be varied continuously. Suppose you mix five elements in 1 at.% steps. How many compositions are there? Counting them is the same as counting the ways to split 100 marbles among 5 boxes, and the answer is 4,598,126. For eight elements it is 26,075,972,546 Our calculation (counting each element as allowed to be 0 at.%. Real alloys often leave out elements or limit their ranges, so treat this as a rough upper bound).

On top of that, the conditions of melting, casting, rolling and heat treatment multiply the possibilities. That is what the "vast map" analogy means. Instead of trying everything, we use machine learning that learns trends from past data to narrow down where to try next. The review by Hart and co-workers states that the pairing of machine learning and alloys has spread to metallic glasses, high-entropy alloys, shape memory alloys, magnets, superalloys, catalysts and structural materials, and that it summarizes both theoretical predictions and experimental validations Sourced [Reference 1].

View original SVG, values and sources

Original SVG reference: Concept diagram (vector illustration). The path from composition to properties, and what is and is not often recorded. The examples in the boxes are our own illustration, not the process of a specific alloy.

(2) Why they are hard: few data and many hidden variables

As the figure shows, the properties of an alloy are set along the chain "composition, processing, heat treatment, microstructure, properties". Yet what is easy to find in papers and databases is only the composition, the main heat-treatment conditions and the final results. The microstructure in between (grain size, precipitates), the distribution of inclusions, the position the specimen was taken from and residual stress are often not recorded (commentary).

A second difficulty is bias in how similar the data are to each other. A common structure is that many heats of the same steel grade sit together, while different grades are far apart. To study scatter, the NIMS fatigue data sheets tested several heats for each grade (in the early editions, more than ten heats per grade) Sourced [Reference 3]. This is valuable data, but when you use it for machine learning you must watch for the fact that "another heat of the same grade" easily ends up on both the training side and the test side (chapter 5).

3. Who does what: calculation, AI and experiment

Three parties appear in alloy design: "calculation", "AI" and "experiment". In this article we divide their roles as follows (the division used throughout this series).

View original SVG, values and sources

Original SVG reference: Concept diagram (vector illustration). The roles of calculation, AI and experiment, as used throughout this series. AI is a tool that narrows where to look; it does not "invent" materials.

• Calculation: phase-diagram calculation (CALPHAD) computes the stability of phases from thermodynamic databases. First-principles calculation (DFT) is a physical simulation that computes properties from the behaviour of electrons. Both include approximations and may not agree with measurements.
• AI: learns trends from past data and proposes candidates to try next. Methods that also give how certain a proposal is (Gaussian processes, ensembles and so on) can tune whether to "try places not yet tried" or to "dig near where a hit was found". In the shape memory alloy search, an adaptive design that makes this "balance of exploitation and exploration" explicit was used Sourced [Reference 8].
• Experiment: make the proposed compositions and measure them. Feeding the results back into the data updates the next proposal (a closed loop). Most cases in this article include this "feeding back" step.

In the cast aluminium example, the three parties form one flow. Phase-diagram calculation gave the microstructure, this was added to the training data of a neural network, and together with a few experimental results Bayesian optimization chose the next composition Sourced [Reference 9] (chapter 6). Calculation "gives candidates cheaply and fast", AI "narrows where to look", and experiment "checks whether it is true".

4. Steel data: fatigue strength and the Matbench yield-strength task

Steel is one of the structural materials with the most complete datasets in MI research. Here we read two examples that use public data. Both are about prediction accuracy; neither is about making a new steel. To understand the numbers, we first explain two indicators with a small example.

(1) NIMS rotating-bending fatigue data (Agrawal et al., 2014)

NIMS (National Institute for Materials Science, Japan) publishes fatigue data sheets for structural materials. According to a 2019 review, there were 126 data sheets at that time, covering carbon steels, low-alloy steels, stainless steels, high-strength steels, aluminium alloys, titanium alloys and others, with several heats tested per grade to examine scatter. They were once viewable on MatNavi and were to be published on NIMS's Materials Data Repository (MDR) Sourced [Reference 3].

Agrawal and co-workers used part of these data to predict the fatigue strength of steel (rotating-bending fatigue, strength at 10⁷ cycles) from composition and processing conditions Sourced [Reference 2].

• Data: 437 records: 371 carbon and low-alloy steels, 48 carburizing steels and 18 spring steels. There are 25 inputs: composition (wt.% of C, Si, Mn, P, S, Ni, Cr, Cu, Mo), upstream processing (ingot size, reduction ratio, inclusions) and heat treatment (normalizing, through-hardening, carburizing, tempering temperatures, times and cooling rates).
• Methods: 12 kinds (linear regression, support vector machine, decision trees, neural network, multivariate polynomial regression and others).
• Validation: LOOCV (leave-one-out cross-validation): hold out one record, learn from the rest, and predict the held-out record, one record at a time.
• Result: MAE ranged from 18.6 to 46.0 MPa and R² from 0.90 to 0.98. The top methods (multivariate polynomial regression, M5 model tree, neural network, REPTree) had R² above 0.97. The authors say accuracy improved over earlier work on the same data (R² of 0.88 to 0.94).

This is a good result as a prediction inside the data. But from what the paper describes, we read it with the following cautions (commentary from here on).

• The data fall into groups by steel grade (carbon and low-alloy, carburizing, spring). The paper also says clustering showed three groups [Reference 2].
• LOOCV leaves other specimens of the same heat and grade on the training side. This check cannot measure the ability to predict a "new steel grade" or a "new heat".
• We did not check whether the comparison with the earlier work used the same validation.

(2) The Matbench steels task: predicting yield strength from composition alone

Matbench is a common problem set for comparing methods that predict materials properties. Dunn and co-workers released it in 2020. It has 13 tasks (from 312 to about 132,000 records, from 10 data sources), and every task is evaluated with the same 5-fold nested cross-validation Sourced [Reference 4]. The steels task has 312 experimental records and is a regression predicting the yield strength (MPa) of steel from composition alone. The data come from a dataset of mechanical properties of steels provided by Citrine Informatics (Conduit and Bajaj, 2017) [References 4, 5].

On the official leaderboard (checked 22 October 2026), the baseline that "always answers the mean of the training data" (Dummy) has an MAE of 229.7 MPa, and the submitted methods range from 79.9 MPa (TPOT-Mat) to 143.0 MPa (gptchem) Sourced [Reference 5]. Every method has a smaller error than the "answer the mean" baseline, but a gap of tens of MPa on average remains.

5. A pitfall in splitting data: when lots of the same grade fall on both sides

Evaluating machine learning rests on testing the model on "data not used for learning". But alloy data contain many similar specimens of the same grade and heat. If you split the data at random, the "siblings" of every test specimen stay on the training side, and a high score comes just from borrowing the answer from next door (commentary).

Meredig and co-workers pointed this out in the context of materials discovery and reported that conventional machine-learning metrics overestimate performance for materials discovery. They proposed cross-validation that holds out a whole cluster of similar items (LOCO CV) Sourced [Reference 18]. Dunn and co-workers also say that cross-validation that splits by group is closer to the real use of predicting "chemical systems with no data" [Reference 4].

We reproduced this phenomenon with synthetic data small enough to check by hand.

• Data (made up): 12 steel grades, 25 heats each, 300 records in total. The centres of four inputs (numbers imitating composition and processing) are placed far apart per grade, and each grade is given a level offset that does not appear in the inputs (standard deviation 70 MPa). Heat-to-heat scatter is small and measurement noise is 12 MPa.
• Models: a "nearest-neighbour" model that answers with the average of the 3 closest records, and "linear regression" that fits a straight line.
• Evaluation: a random 5-fold split, and a split that holds out one whole grade.

Result (random seed 0): for nearest neighbours, R² was 0.978 (MAE 11.5 MPa) with the random split and -0.21 (MAE 76.0 MPa) with a grade held out. The medians over 20 random seeds are 0.976 and -0.31 (the range with a grade held out was -1.18 to 0.48). Linear regression gave 0.63 and -0.29 (seed 0): a straight-line fit also cannot pick up the level offset of each grade, so it did not work on an unseen grade Our calculation.

Our calculation. Python (NumPy), double precision. The data are made up for this article and are not properties of real steel. The point is not the size of the numbers but that "the same model can look very good, or worse than answering the average, depending only on the split".

6. Designs verified by experiment: superalloys, shape memory alloys, cast aluminium, steel, high-entropy alloys

From here we read cases where "an alloy proposed by AI was actually made and measured". For each case we separate who made how many alloys, what was measured and what it was compared with. The numbers are as stated in the abstract or text of each paper.

(1) Searching for shape memory alloys by adaptive design (Xue et al., 2016)

In NiTi-based shape memory alloys, the transformation temperature differs between heating and cooling (thermal hysteresis, ΔT). A smaller gap is generally considered favourable for repeated use. Starting from 22 records of existing data, Xue and co-workers proposed the next composition, made and measured it, and fed the result back, repeating this 9 times. The search space was about 800,000 compositions. They made and measured 36 compositions, and 14 had a smaller ΔT than any of the original 22. The smallest was 1.84 K, for Ti50.0Ni46.7Cu0.8Fe2.3Pd0.2 Sourced [Reference 8].

(2) A nickel-base superalloy and a molybdenum-base alloy meeting several conditions (Conduit et al.)

Conduit and co-workers built a computational tool that trains a neural network on existing data, predicts each property from composition and heat treatment, and searches for the alloy most likely to meet the targets. In designing a polycrystalline nickel-base superalloy they considered up to eleven conditions at once: cost, density, amount and solvus temperature of the γ′ phase, phase stability, fatigue life, yield stress, ultimate tensile strength, stress rupture, oxidation resistance and elongation. The authors report that experimental data show the proposed alloy meets the computed predictions and, in particular, exceeds commercial alloys in oxidation resistance and yield stress Sourced [Reference 6]. In the following molybdenum-base alloy, a similar design was done with the conditions of cost, phase stability, precipitate content, yield stress and hardness, and the authors report that its physical properties exceed commercial molybdenum-base alloys for forging dies [Reference 7].

The point to note is that cost and phase stability are among the conditions. The design looks for "an alloy that is strong within what can be made and bought", not just "a strong alloy". On the other hand, the abstracts do not give the number of experiments, the names of the commercial alloys compared, or the numerical values. We could not confirm the full text, so we do not quote numbers (an item we could not confirm).

(3) A cast aluminium alloy linking computational thermodynamics, machine learning and experiment (Zhang et al., 2023)

Zhang and co-workers designed the addition of Ti to an Al-Si-Mg-Sr casting alloy (A356-0.005Sr) to raise strength and ductility at the same time, combining phase-diagram calculation (CALPHAD), machine learning and experiment within a Bayesian optimization framework. They made six alloys with different Ti contents, used their measured mechanical properties for learning, and the recommended Ti content was 0.08 wt.%. When that composition was actually made and measured, the ultimate tensile strength was 199.6 MPa, the 0.2% yield strength 101.6 MPa and the elongation 12.3%, and the authors say this agreed well with the prediction Sourced [Reference 9].

This example shows that "even with small data, calculation and experiment together can narrow things down", but the only variable moved was the amount of Ti (in a low-addition range), so it is not a high-dimensional search (commentary). We did not check details such as the heat-treatment state of the specimens.

(4) A TWIP steel designed from literature data (Zhou et al., 2024)

Zhou and co-workers compared several machine-learning methods on 273 literature records for TWIP (twinning-induced plasticity) steel and built models predicting yield strength, tensile strength and elongation. Using SHAP analysis (a way to measure how much each input affected a prediction) and multi-objective optimization, they designed two new TWIP steels and made and measured them by a conventional route (hot forging, hot rolling, cold rolling and annealing). Yield strengths were 585 and 560 MPa, tensile strengths 1,055 and 1,101 MPa, and elongations 55% and 58.5%. The authors state that the yield strength, a known weakness of TWIP steel, was improved while the product of strength and elongation (58.0 and 66.4 GPa%) was kept Sourced [Reference 10]. We did not check the numerical values of the conventional TWIP steels used for comparison.

(5) High-entropy alloys and superalloys, updated with few experiments

• Raising hardness (Wen et al., 2019): in the Al-Co-Cr-Cu-Fe-Ni system, combining a machine-learning surrogate model with an experimental design method, they report making an alloy 10% harder than the best value in the original training data in only seven experiments. They also say that using descriptors based on alloy properties, as well as composition, worked better than composition alone Sourced [Reference 11].
• An Invar alloy with low thermal expansion (Rao et al., 2022): with closed-loop active learning that combines machine learning, DFT, thermodynamic calculations and experiments, they made and measured 17 new alloys out of millions of possible compositions, and report finding two high-entropy Invar alloys with an extremely low thermal expansion coefficient of about 2 × 10⁻⁶ K⁻¹ at 300 K Sourced [Reference 12].
• γ′ solvus temperature of superalloys (Liao et al., 2024): starting from sparse data, using clustering and other unsupervised learning, they report finding nine new superalloys whose chemistries differ from those in the training data, and three of them had a γ′ solvus temperature about 50 °C higher. It is an attempt to make up for the weakness of prediction-centred searches, which tend to stay inside the data (interpolation), by sampling aimed at extrapolation Sourced [Reference 13].

The definition and properties of high-entropy alloys are covered in detail in our explainer on high-entropy alloys. What we want to point out here is not how large the results are but how many experiments, and for which property, were used to verify. Hardness, thermal expansion coefficient and γ′ solvus temperature are each a single property; they do not verify the other properties needed to use the alloy as a structural material (toughness, corrosion resistance, workability, cost and so on) (commentary).

(6) The cases side by side: what was verified, how many, and how far

All Sourced (abstracts and text of each paper, checked 22 October 2026). The right-hand column is our commentary. The arrangement of the table is Our calculation (organization).

7. Cases that stop at calculation, and composites

(1) Confirmation by calculation and confirmation by experiment are different

Pei and co-workers used a dataset of 1,252 multicomponent alloys to predict by machine learning whether a solid solution forms, and report an accuracy of 93%. They also built a new rule with a physical basis that uses only elemental properties (accuracy 73%), predicted solid solutions for combinations in three blocks of nine elements each, and say the agreement with phase-diagram calculation (CALPHAD) was 94% Sourced [Reference 14].

What was used for confirmation here was another calculation (CALPHAD), not an experiment measuring newly made alloys. Nor does the abstract say with what split (random, or by composition system) the 93% was obtained, and we did not check it. Kaufmann and Vecchio's ML-HEA was also validated by comparing the model with reliable experimental data for binary to quinary systems, and compared with methods such as CALPHAD Sourced [Reference 15]. This is comparison with existing experimental data, not measurement of newly made alloys.

Agreement between calculations shows that "the prediction is consistent with another calculation". That is an important check, but it is different from confirming that a real alloy can be made and shows the intended property (commentary).

(2) Composites: create data by simulation, then print and test

For composites (combinations of hard and soft materials and so on), experimental data are scarce, so some studies create data by finite-element analysis (FEA). Gu and co-workers trained a convolutional neural network on finite-element data for hundreds of thousands of structures, used a self-learning algorithm to create microstructural patterns of hierarchical materials that are stronger and tougher, and report that they confirmed this by additive manufacturing (3D printing) and testing Sourced [Reference 16]. The review by Chen and Gu summarizes, as an outlook, progress in applying machine learning to the analysis and design of composites [Reference 17].

How to read it: the training data in the work of Gu and co-workers are simulations, not experiments, and the tests were done on printed specimens. For structural fibre-reinforced composites (such as carbon-fibre-reinforced plastics), we could not find, within our search, a case where a machine-learning design proposal was made and tested. Composites are set by many factors (stacking sequence, fibre orientation, moulding conditions, interfaces), so designing the input is harder than for metal alloys (commentary).

8. A materials engineer's view: your own data and experiment design

From the cases so far, we pick out three points that help when you use your own alloy data for machine learning. All of them are our commentary, not an official guideline.

9. Limits, what we could not confirm / summary

(1) Depth of checking of the papers

We checked the review by Hart and co-workers, the two papers by Conduit and co-workers, the paper by Wen and co-workers, the paper by Kaufmann and Vecchio and the review by Chen and Gu within the abstract (or a published summary). We read the text of the papers by Agrawal and co-workers and by Dunn and co-workers, the review by Furuya and co-workers and the paper by Zhang and co-workers (the results numbers). The papers by Rao and co-workers, Liao and co-workers and Xue and co-workers were checked within the abstract. We did not check the validation procedure in the text (split, uncertainty, basis of comparison).

(2) Independent replication

For the cases in chapter 6, we could not find replication by an independent laboratory or reproduction on a different lot. We treat them as claims of the papers.

(3) Practical use and mass production

We could not confirm from primary sources that a proposed alloy was adopted in a part or standard or mass-produced. We have not written "commercialized" claims that rest only on announcements by companies or institutes.

(4) What we did not cover

Atomistic simulation of alloys with machine-learning interatomic potentials, process optimization in additive manufacturing, machine learning for corrosion, hydrogen embrittlement and fatigue cracks, and control of steelmaking processes are not covered. MLIPs are covered in our explainer on machine-learning interatomic potentials. Apart from the Matbench steels task (312 records, composition only), we did not confirm any common benchmark specific to alloys.

(5) Comparing numbers

Data, splits, metrics and test conditions differ from paper to paper. This article does not rank any method, alloy or research group.

10. How to read the yardsticks and standards

The quality of MI for alloys is measured with three yardsticks: prediction error (MAE, R²), how the data were split, and whether and how many alloys were verified by experiment. Error shows "how far it misses on average", the split shows "whether it also holds for new steel grades or compositions", and experimental verification shows "whether the alloy could really be made and measured". No single one of them tells the whole story. Meanwhile, measurements themselves have mechanical-testing standards (ISO, JIS). These define test methods; they do not decide how good an AI prediction is. We could not find a standard specific to MI for alloys. The checking date is 22 October 2026.

The arrangement of the table is Our calculation (organization). Numbers, titles, publication dates and status of standards were checked on the official ISO pages and the JIS search of the Japanese Industrial Standards Committee (JISC) (checked 22 October 2026). The full texts are paid, so we stay with the scope statements. ASTM standards are not covered in this article, and we did not consult the ASTM site.

Cautions when reading (for materials engineers)

• A leaderboard score is not the strength of your own alloy: the top methods in the Matbench steels task give numbers for 312 records with composition only. It is worth re-measuring on your own grades, your own processing conditions and your own tests.
• Prediction and experimental verification are different questions: even with a high R², it remains a "prediction" until you make and measure the alloy. Conversely, one hit in an experiment must be checked for chance with repeats and a control.
• A standard is a "test method" and does not guarantee "alloy quality": ISO 6892-1 and ISO 1143 define how to measure. Even a value from a "test following the standard" changes with specimen, edition and conditions. The FAIR principles are also a recommendation and do not guarantee that data are correct.
• Plans and achievements differ: the 2026 edition of ISO 1099 was published only in October 2026. The old edition (2017) is withdrawn. When you quote a measured result, add the edition of the standard.

11. Glossary

12. References (primary sources)

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13. Liao W., Yuan R., Xue X., Wang J. et al. "Unsupervised learning-aided extrapolation for accelerated design of superalloys", npj Computational Materials 10, 171 (2024), DOI 10.1038/s41524-024-01358-8 (open access, abstract checked) - doi.org/10.1038/s41524-024-01358-8
14. Pei Z., Yin J., Hawk J. A., Alman D. E., Gao M. C. "Machine-learning informed prediction of high-entropy solid solution formation: Beyond the Hume-Rothery rules", npj Computational Materials 6, 50 (2020), DOI 10.1038/s41524-020-0308-7 (open access, abstract checked) - doi.org/10.1038/s41524-020-0308-7
15. Kaufmann K., Vecchio K. S. "Searching for high entropy alloys: A machine learning approach", Acta Materialia 198, 178-222 (2020), DOI 10.1016/j.actamat.2020.07.065 (abstract checked) - doi.org/10.1016/j.actamat.2020.07.065
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21. ISO "ISO 1143:2021 Metallic materials - Rotating bar bending fatigue testing" (ISO page) - iso.org/standard/79575.html
22. ISO "ISO 1099:2026 Metallic materials - Fatigue testing - Axial force-controlled method" (ISO page) - iso.org/standard/85731.html
23. Japanese Industrial Standards Committee (JISC) JIS search (numbers and titles of JIS Z 2241 and JIS Z 2274 checked; titles in Japanese) - jisc.go.jp/app/jis/general/GnrJISSearch.html
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13. Claim-to-source audit

Last updated: 22 October 2026 / Sources are limited to primary ones (peer-reviewed papers, arXiv preprints, official data-publication pages, and the official ISO and JISC pages). The full texts of ISO standards are paid and were not checked. The synthetic-data examples are calculations on data made up for this article, not the performance of real alloys. Independent replication, practical use and mass production, some numbers in the text of certain papers, demonstrations on real composite structures, and a standard specific to MI for alloys could not be confirmed and are therefore not stated. The figures are explanatory concept diagrams, drawings that include our own calculation, or plots of published numbers; Fig. 1 is a frame for an AI-generated image (image not yet placed).