materials-chemistry/ai produced the result/Nature Communications 2016 · v2
Machine learning picked which shape-memory alloys to make next, round by round
Researchers searched a space of 797,504 possible nickel-titanium alloy recipes for ones with low thermal hysteresis. Models trained on measured alloys predicted each candidate's value and its uncertainty, and those predictions chose all 36 recipes that were actually made.
spectrum · one line per step, placed by what the step does · bright lines used AI
Accelerated search for materials with targeted properties by adaptive design
Nature Communications, 2016
doi:10.1038/ncomms11241 · record aix-00016 v2 · checked 2026-10-07
- AI was for
- Property prediction, Experimental design
- Model family
- Support vector machine, Gaussian process
- Checked by
- Experimental36 tested, 14 worked
- Code
- not reported
The finding the paper is about came from the AI.
What this research was about
Shape-memory alloys are metals that switch between two crystal arrangements when heated or cooled, which lets a bent piece spring back to a remembered shape. The switch does not happen at the same temperature in both directions. That gap is called thermal hysteresis, and a wide gap wastes energy and tires the metal out over repeated cycles. Making the gap small is desirable, but it depends on the exact proportions of the metals in the mix, and there is no simple rule linking recipe to behaviour. Each candidate recipe has to be melted, treated and measured, so only a handful can ever be tested.
The work concerned a family of alloys built on titanium and nickel, with small amounts of copper, iron and palladium substituted in. Constraining the proportions still left 797,504 possible compositions. Twenty-two of these had already been made in the group and their hysteresis measured by calorimetry, a technique that tracks heat taken in or given out as a sample warms and cools. The task was to use those few measurements to decide which untested recipes were worth the effort of making.
Where AI came in
Each recipe was turned into a short list of numbers describing its ingredients, using tabulated properties of the elements such as atomic radii, electronegativity and valence electron count. Models were then trained on the 22 measured alloys to map those numbers to measured hysteresis: a Gaussian process model and support vector regression with two different kernels, all built from scratch using the scikit-learn library. Repeated resampling of the training data gave each prediction an uncertainty alongside its value. Candidate model-and-selector pairings were compared by cross-validation, and support vector regression with a radial basis function kernel, paired with a Knowledge Gradient selector, was chosen.
The trained model was then run across the unexplored compositions, giving a predicted hysteresis and a spread for each. A selector ranked candidates by how much improvement they might offer, balancing a promising prediction against an uncertain one, and four recipes were picked per round. Those four were melted, heat treated and measured, and the new measurements were added to the training set before the next round. Nine rounds were run, so the model stood in for the judgement that would otherwise decide which experiment to do next. Of 36 compositions made this way, 14 had hysteresis below 3.15 K, the lowest in the starting data, and one reached 1.84 K.
Written by AIxSci from the checked record below, to give context for readers outside the field. It is not part of the record.
The work
Technical · from the record
An adaptive design loop paired support vector regression on composition-derived features with a selector that maximized expected improvement, to choose which NiTi-based shape memory alloy compositions to synthesize next. Starting from 22 alloys with measured thermal hysteresis and a constrained space of 797,504 possible compositions, nine iterations were run, with four predicted compositions synthesized and measured by calorimetry in each. Of the 36 compositions synthesized, 14 had thermal hysteresis below 3.15 K, the lowest value in the original data set, and Ti50.0Ni46.7Cu0.8Fe2.3Pd0.2 had a measured ΔT of 1.84 K. Density functional theory calculations were then used to compare austenite-martensite energy differences and activation barriers for the relevant transformations.
How AI was used
Each alloy in the Ni50−x−y−zTi50CuxFeyPdz space was described by six composition-weighted elemental features (pseudopotential radii, Pauling electronegativity, metallic radius, valence electron number, Clementi atomic radii, Pettifor chemical scale). Regressors implemented in scikit-learn — a Gaussian process model and support vector regression with radial basis function and linear kernels — were fitted to the measured training alloys to map features to thermal hysteresis, with uncertainties obtained from bootstrap sampling for the support vector models. Candidate regressor:selector pairs were compared by cross-validation on the training set, counting the average number of picks needed to find the best training alloy over 2,000 repeats, and SVRrbf with the Knowledge Gradient selector was chosen. The trained model was then run over the unexplored compositions using 1,000 bootstrap samples to give a predicted mean and standard deviation per alloy, and the selectors (expected improvement, Knowledge Gradient, or pure minimum) ranked candidates; four compositions per round were drawn using the Kriging believer scheme, which successively adds the top prediction to the data set before re-predicting. The four alloys were arc melted, heat treated and measured, and the measurements augmented the training set for the next round of fitting and selection over nine rounds. Separate planewave density functional theory calculations with the virtual crystal approximation were used afterwards to examine energetics and strains, and involved no learned model.
The shape of the work
Structural · the record, drawn
no AI
Build initial measured alloy data set
Obtaining raw data, whether by measurement, download or retrieval.
We synthesized 22 (training set) out of 797,504 possibilities in our group under identical conditionswhere the paper describes this · verbatim
no AI
Encode alloys as composition-weighted features
Encoding data into features, descriptors, embeddings or graphs.
Each Ni50−x−y−zTi50CuxFeyPdz alloy in our composition space was uniquely described as a weighted fraction of each of these featureswhere the paper describes this · verbatim
AI
Train regressors and select regressor:selector pair
Fitting model parameters, including fine-tuning an existing model.
we investigated the performances of several regressor:selector combinations as a function of the size of the data using cross-validationwhere the paper describes this · verbatim
AI
Predict hysteresis and uncertainty across search space
Running a trained model over new data to predict, classify or score. The AI stood in for physical experiment.
We predicted ΔT (using SVRrbf) for all the data in the search space using 1,000 ‘bootstrap' sampleswhere the paper describes this · verbatim
no AI
Select next four alloys by expected improvement
Iterative search over a space.
The design chooses the ‘best' four candidates for synthesis and characterization.where the paper describes this · verbatim
no AI
Synthesize and characterize selected alloys
Physical execution, by hand or by robot. Its result feeds back into an earlier step.
We synthesize and characterize 36 predicted compositions (9 feedback loops) from a potential space of ∼800,000 compositions.where the paper describes this · verbatim
no AI
Density functional theory analysis of transformations
Numerical or physics simulation, including where a learned surrogate replaces it.
DFT calculations for the NiTi SMAs were performed with non-spin polarized generalized gradient approximation (GGA) calculationswhere the paper describes this · verbatim
What the record says
Technical · every part carries its own basis
+ in the paper~ our reading− not reported
How to read the quotations. A quotation shows where the paper describes something. It does not quote every value beside it: one passage locates a part of the work, and values without their own quotation are our reading of that passage.
All 36 synthesized compositions, including the reported lowest-hysteresis alloy, were chosen by the trained regressor plus selector; the finding is the output of that loop
we used several well-known regressors including a Gaussian Process Model (GPM)where the paper describes this · verbatim
We found 14 new alloys, out of 36 synthesized compositions from 9 feedback loopswhere the paper describes this · verbatim
Details and data are provided in Supplementary Note 4.where the paper describes this · verbatim
What this paper did not report
Technical · absence is published deliberately
- CodeWhether the code is available is not stated.
- Trained model weightsWhether the trained model is available is not stated.
- ComputeThe hardware or time used is not stated.
- Version of Support vector regression with radial basis function kernel (SVRrbf)Which version of the model was used is not stated.
- Version of Support vector regression with linear kernel (SVRlin)Which version of the model was used is not stated.
- Version of Gaussian Process Model (GPM)Which version of the model was used is not stated.
- What step 3 replacedThe paper gives no basis for what the AI stood in for.
About this article
Record aix-00016, version 2, checked by a person on 2026-10-07. The record describes the paper; it does not assess whether the paper's findings are right. The paper is published under CC-BY-4.0; quotations are at most 25 words. How we work · Report an error