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Which alloy composition,what process parameters? Inferring the recipe from optimized metallic microstructure and texture

Mahish K. Guru, Jan Bohlen, Louam Lemjid, Marius Tacke, Roland Aydin, Noomane Ben Khalifa

arXiv:2610.08165v1cs.AIcond-mat.mtrl-scics.CE

TL;DR

Recovering the alloy composition and process from an optimized microstructure still relies on expert knowledge. The paper compares three descriptors and prediction heads on measured magnesium-alloy extrusion conditions; catalogue-aware heads improve the descriptors, with conventional statistics strongest on composition and microstructure reducing process-temperature error.

  • Problem

    Recovering the recipe that produced a microstructure—its alloy composition and processing parameters—remains a largely expert-driven step in alloy development.

    Source: §1 · p. 2

  • Method

    The study compares conventional statistics, a frozen vision embedding, and a grain-graph network on two conditional recipe-prediction tasks using a measured campaign of 107 conditions across 14 alloys.

    Source: §1 · p. 2

  • Results

    Catalogue-aware heads improved every descriptor; conventional reranking reached 13.6% WAPE versus 16.8% for fusion and 30.0% for retrieval, while microstructure reduced temperature MAE from 69.7 to 35-38 °C.

    Source: §6 · pp. 6–7, §7 · p. 9

  • Takeaways & Limitations

    Optical microscopy and X-ray pole figures can suffice to walk the recipe leg and provide a check in a self-driving laboratory.

    Source: §7 · p. 9

    The composition task selects only among 14 known alloys, and the study has only 107 conditions from one alloy system and process.

    Source: §7 · p. 9

Abstract

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The mechanical properties of a metallic alloy are set by its microstructure and texture: the size and shape of its grains and the orientation of their crystals. That structure is in turn set by a recipe, the alloy composition together with the processing parameters. Alloy development runs this chain forwards, tuning the structure until a target property is met. Running it backwards, from an optimized structure to the recipe that would produce it, still relies on expert knowledge. We ask whether this backwards step can be learned. On an in-house dataset of 107 magnesium alloy extrusion conditions across 14 alloys, each with optical micrographs and an X-ray texture measurement, we compare three descriptors of microstructure and texture: conventional grain and texture statistics, a vision embedding from a pretrained image encoder, and a graph neural network on the grain network. Each is paired with prediction heads for two tasks: the alloy composition given the process (Task A), and the process parameters given the composition (Task B). Under 5-fold cross-validation, the conventional descriptors identify the correct alloy for 65% of held-out conditions, against 17% for always guessing the most common alloy, while the learned embeddings stay below 30%. The process parameters are recoverable but noisier: compared with using the composition alone, the microstructure roughly halves the temperature error. Because only a few alloys were cast and only a few press settings were used, both answers are discrete, and heads that pick from these known options, while respecting their order, worked better than heads that predict a free value.

1 Introduction

The paper studies the missing recipe leg: inferring alloy composition and processing parameters from microstructure and texture. It evaluates this question on measured magnesium-alloy extrusion conditions using three descriptors and two conditional prediction tasks.

1 Introduction

  • The recipe leg—recovering the composition and process that produced an optimized structure—remains dependent on expert knowledge.The paper frames it as the missing first link in a chain from recipe to structure to mechanical properties.Source: §1 · pp. 1–2
  • In automated characterization and self-driving laboratories, recipe recovery could support quality control, anomaly detection, and planning the next experiment.The proposed check uses images already collected and could flag mislabelled samples, press drift, or repeated conditions.Source: §1 · p. 2
  • The measured campaign contains 107 extrusion conditions across 14 magnesium-alloy classes, each with optical micrographs and an X-ray texture measurement.Although composition and process appear continuous, only 14 alloys were cast and the press used a short list of settings.Source: §1 · p. 2
  • The study compares conventional statistics, a frozen vision embedding, and a grain-graph network for composition-given-process and process-given-composition prediction.It also compares prediction heads that choose among known alloys and press settings with heads that do not impose that catalogue.Source: §1 · pp. 2–3, Figure 1 · p. 2

2 Related work

Prior work has mainly modeled structure-to-property, property-to-structure, or forward process-to-structure relationships. This paper instead asks whether the full recipe can be recovered across multiple alloys from experimental microstructure data.

2 Related work

  • Most microstructure-learning work predicts properties from structure, proposes structures for target properties [13], or reconstructs structures matching measured statistics.Process-structure linkages have also mostly been studied in the forward direction, often using simulated data.Source: §2 · p. 3
  • Image-classification studies infer processing labels for individual material systems [18], while this work targets composition and process across 14 alloys.The paper compares domain-designed and learned descriptors on an experimental campaign of tens to hundreds of conditions with labels drawn from short lists [8, 11].Source: §2 · p. 3

3 Data: sparse by construction

The dataset pools measured wrought-magnesium extrusion campaigns, but its composition and process labels are sparse and partly confounded by experimental design. Evaluation is condition-grouped so images from one condition cannot appear across training and test folds.

3 Data: sparse by construction

  • The dataset contains 107 conditions from measured extrusion campaigns, with eight-element alloy compositions, temperatures from 200 to 500 °C, ram speeds from 0.5 to 7.5 mm/s, optical micrographs, and ODFs.The conditions cover AZ31, Zn-bearing alloys, ME21, and Mg-Gd and Mg-Gd-Mn families.Source: §3 · p. 3
  • Composition labels are sparse across eight possible elements, while process settings are sparse and confounded because each alloy family used its own temperature and speed grid.A composition-only baseline measures how much process prediction can exploit that design correlation without microstructure.Source: §3 · p. 3
  • Task A predicts element weight percentages from structure plus known temperature, log speed, and an extrusion-ratio flag; Task B predicts temperature and speed from structure plus known composition and the flag.Every branch also receives the known half of the recipe, with its input width varying by branch and prediction head.Source: §3 · p. 4, Table 1 · p. 4
  • Condition-grouped 5-fold cross-validation keeps all images from each condition in one held-out fold, avoiding image-level leakage between training and test sets.A validation part of each training fold selects hyperparameters, and other choices use out-of-fold predictions.Source: §3 · p. 4

4 Method: microstructure and texture descriptors

Three descriptor pipelines represent the same measured microstructure and texture in different forms: conventional statistics, a vision embedding, and a grain graph. The learned branches use representative volume elements built from measured grain distributions and texture.

4 Method: microstructure and texture descriptors

  • The two learned branches see grain arrangements reproduced in an RVE whose grain distributions follow the micrograph and whose orientations are sampled from the measured ODF.The vision encoder reads an orientation-coloured map, while the graph encoder reads a segmented grain network; all three branches receive texture.Source: §4 · p. 4, Figure 2 · p. 5
  • The conventional branch extracts 438-D grain and texture statistics directly from the micrograph, grain mask, and measured ODF.Its components include spatial correlations, reduced CNN Gram matrices, grain-shape distributions, and reduced spherical-harmonics coefficients.Source: §4 · p. 4
  • The frozen vision branch maps orientation-coloured RVE images to a 1280-D embedding using the Co-PiLOT encoder [13].The encoder was trained on about 80k EBSD-derived microstructures, and its flattened tokens are used without fine-tuning on the 107 conditions.Source: §4 · pp. 4–5, Figure 2 · p. 5
  • The grain-graph branch represents RVE grains as nodes and shared boundaries as edges, then uses a graph-attention encoder to produce a 128-D embedding.The encoder uses grain geometry and orientation, boundary length and misorientation, and attention pooling to eight tokens per image.Source: §4 · p. 5, Figure 3 · p. 5

5 Method: prediction heads

The heads choose between catalogue-based and continuous answers from the same microstructure descriptor, with baselines that omit microstructure. Task A predicts alloy composition, while Task B predicts temperature and extrusion speed together.

5 Method: prediction heads

  • Heads choose from the known alloys or settings (the catalogue) or predict freely, using the same descriptor inputs and folds.Two no-microstructure baselines are the most frequent training answer and a classifier that sees only the known half of the recipe.Source: §5 · p. 6
  • Task A compares retrieval, condition-balanced fusion, and a reranker that blends fusion with a second classifier when eligible.The reranker uses out-of-fold predictions to select its blend weight; if no eligible weight is found, it keeps fusion unchanged.Source: §5 · p. 6
  • Task A reports present-element WAPE alongside all-element WAPE and macro false-positive rate to guard against heads that predict every element as present.Source: §5 · p. 6
  • Task B compares GBDT and ARD GP predictions with a joint-grid GP that returns an observed temperature–speed pair minimizing expected relative error.The other heads' speed estimates are also snapped to one of the eleven observed speeds.Source: §5 · p. 6

6 Results

The conventional descriptor was strongest for alloy composition, while the joint-grid GP improved process estimates over a composition-only baseline. Performance remained constrained by sparse examples at extreme speeds, and guard metrics exposed misleading composition predictions.

6 Results

  • The conventional Task A reranker assigns higher probability to the true alloy than the learned branches, which put little probability on it for many conditions.Figure 4 pools confidence over 107 held-out conditions; farther right is better.Source: §6 · p. 6, Figure 4 · p. 7
  • 13.6% WAPE for the conventional reranker beat fusion (16.8%) and retrieval (30.0%), with best top-1 (0.646) and fewest false positives (1.1%).Source: §6 · p. 6, Table 2 · p. 7
  • 0.17 top-1 for the majority-alloy baseline and 0.13 for the process-only classifier; learned branches reached about 1.6 times the majority rate, with NLL 2.23 to 2.30 versus 2.54 for the class prior.Source: §6 · p. 7
  • Against the composition-only baseline, the joint-grid GP reduced temperature MAE from 69.7 to 35-38 °C and log speed error from 0.75 to 0.42-0.45.Conditions within one speed setting rose from 26% to 46-52%; its log MAE corresponds to a typical factor of about 1.55.Source: §6 · pp. 7–8
  • Figure 5 compares predicted with true velocity: both heads undershoot fast conditions, while temperature predictions saturate above about 400 °C.Source: Figure 5 · p. 8, §6 · p. 8
  • About two fast examples per alloy family leave the fastest and slowest settings under-recovered; log-space modelling and grid snapping do not recover the tails.The authors identify more information or more extreme-setting conditions as remedies.Source: §6 · p. 8
  • 17.0% WAPE on one split concealed 14% false-positive elements and 67% all-element WAPE for the hurdle and metric-learning heads.The guard metrics exposed the false positives that WAPE alone would miss.Source: §6 · p. 8

7 Conclusion

The recipe leg runs from optimized microstructure and texture back to alloy composition and processing settings. Catalogue-aware heads that preserve the ordering of known choices improved on every descriptor, while conventional statistics were easier for every head to use than learned embeddings.

7 Conclusion

  • Catalogue-aware heads that preserve distances among known recipes improved on every descriptor; heads ignoring the catalogue or its ordering did not.The comparison concerns the recipes actually available in the campaign, not continuous answers.Source: §7 · pp. 8–9
  • Conventional statistics measured on micrographs were easier for every head to use than reconstruction-trained embeddings, while representation-size effects remain unresolved.The paper frames this as a comparison of descriptor pipelines as used, not representation size.Source: §7 · p. 9
  • Optical microscopy and X-ray pole figures suffice for the recipe-leg check in a self-driving laboratory, provided failure modes are reported.The proposed check uses measurements already being collected.Source: §7 · p. 9
  • The composition task selects among 14 known alloys, and the study’s 107 conditions cover one alloy system and process.The authors identify larger campaigns with more alloys as the next step.Source: §7 · p. 9

A Method details

  • The appendix adds descriptor and prediction-head specifications, metrics and baselines, per-fold results, a Task B classification ablation, and error diagnostics.These materials complete the method description and report results omitted from the main text.Source: A Method details · p. 14

A.1 Descriptor specifications

The paper compares a conventional feature pipeline with a frozen vision encoder and a grain-network graph model. The learned branches use synthetic representative volume elements built from each micrograph’s grain statistics and condition texture.

A.1 Descriptor specifications

  • The conventional descriptor has 438 columns spanning spatial correlations, CNN Gram matrices, grain-shape distributions, and ODF coefficients, plus four known-process columns.The 438 columns are reduced or assembled into blocks; the known half of the recipe comprises temperature, log extrusion speed, and extrusion-ratio type.Source: §A.1 · p. 14
  • Both learned branches use one DREAM.3D RVE per micrograph, built from its grain statistics and condition ODF; images with fewer than 10 usable grains are skipped.The generated RVE uses a lognormal equivalent diameter and beta aspect ratio, with orientations sampled from the condition texture.Source: §A.1 · p. 14
  • The vision branch freezes the Co-PiLOT ViT-H encoder and uses its flattened 16 × 80 latent as the descriptor.Figure 7 depicts the frozen encoder mapping an orientation-coloured RVE map to the latent used by the decoder.Source: §A.1 · p. 14, Figure 7 · p. 15
  • The grain-graph branch represents grains as nodes and shared boundaries as edges, then applies four GATv2 blocks and attention pooling.Node attributes include grain geometry, orientation, and location; edge attributes include boundary length and misorientation.Source: §A.1 · p. 15

A.2 Prediction head specifications

The prediction heads map each descriptor to either one of 14 alloy choices or process settings. The study compares catalogue-constrained heads with alternatives and uses training-only out-of-fold predictions for head selection.

A.2 Prediction head specifications

  • Condition-stratified inner splits produce training-only out-of-fold predictions, while held-out test folds do not select hyperparameters.Preprocessing is refitted within each inner split; validation portions select base hyperparameters.Source: §A.2 · p. 15
  • For Task A, image-level alloy probabilities are averaged by condition, and the top alloy’s nominal weight-percent vector supplies the composition prediction.Retrieval instead lets nearby training images vote for an alloy using validation-selected cosine-similarity weights.Source: §A.2 · p. 15
  • Task A condition-balanced fusion averages a process-informed CatBoost classifier with balanced retrieval, then blends that probability with an auxiliary classifier.The reranker selects its blend weight on training-condition OOF predictions subject to not exceeding fusion’s WAPE and macro false-positive rate.Source: §A.2 · p. 15
  • For Task B, CatBoost and an ARD Gaussian process predict temperature and log speed, with the GP pooling descriptors by condition and reducing them by PCA.The ARD GP fits an independent GP per target and applies a lognormal smearing correction to its reported speed point prediction.Source: §A.2 · p. 16
  • The joint-grid GP models temperature and log speed together, then chooses the observed setting pair with the smallest posterior expected relative error.Its kernel combines descriptor features with known composition and extrusion-ratio columns; other heads’ speed predictions can be snapped to observed speed levels.Source: §A.2 · p. 16

A.3 Metrics and baselines

The appendix defines the metrics and baselines used to assess alloy and process predictions, then reports fold-level stability and calibration. The conventional Task A reranker leads across folds, while the joint-grid GP’s intervals are under-dispersed.

A.3 Metrics and baselines

  • Composition WAPE normalizes each element’s absolute error by the amount of that element present, and macro averaging keeps rare elements visible.WAPEall and false-positive rate guard against predicting elements that are absent.Source: §A.3 · p. 16
  • Process scores include temperature and speed errors, exact-speed and within-one-setting rates, temperature hits within ±25 °C, and 90% interval coverage.Log MAE is used for speed because the range spans a factor of 15; exp(log MAE) is its typical multiplicative error.Source: §A.3 · p. 16
  • The most-frequent-answer baseline tests input-free guessing, while the known-half-only baseline measures what process–composition design confounding reveals.Other comparisons include retrieval, standard regressors, and classifiers that retain the catalogue but discard setting order; results use condition-grouped five-fold cross-validation.Source: §A.3 · p. 16, B Additional results · p. 17

B.1 Per-fold tables

  • 20.4% WAPE was the conventional reranker’s worst-fold score, still better than either learned branch’s best fold.The per-fold table supports the comparison; vision WAPE ranged from 28.0 to 73.8% across folds.Source: Table 4 · p. 17, §B.1 · p. 17
  • The joint-grid GP had the smallest fold-to-fold spread on nearly every process row, whereas vision ARD GP velocity MAPE was 120.5 ± 57.2.The latter standard deviation was of the same order as its mean, consistent with error dominated by a few conditions far from observed settings.Source: §B.1 · p. 17

B.2 Calibration

  • The joint-grid GP’s nominal 90% intervals had coverage of about 0.5, while the gnn ARD GP had coverage of 0.69 for temperature and 0.71 for velocity.The authors therefore caution against trusting the winning heads’ uncertainty statements beyond point accuracy.Source: §B.2 · p. 17

B.3 Classification ablation for Task B

The Task B classification ablation finds conventional level classifiers slightly better than the joint-grid GP at exact-speed calls, but their misses can be large. Composition diagnostics show that the conventional branch’s alloy errors are mostly nearby concentration levels, while learned branches’ errors are more dispersed.

B.3 Classification ablation for Task B

  • 30.7% versus 24.0%: conventional level classifiers named exact speed slightly more often than the joint-grid GP, although classifier misses remained large.The classifiers’ share within one setting was 29–36%, barely above the composition-only baseline’s 26%.Source: §B.3 · pp. 17–18, Table 6 · p. 18
  • At 35.0 °C, the GNN pair classifier had the lowest temperature MAE of any head; classifiers’ log speed error was 0.57 to 0.63, between the composition-only baseline and joint-grid GP.The ablation concludes that treating the answer as discrete helps when the head chooses among observed settings and preserves distances between them, as the joint-grid GP does.Source: §B.3 · p. 18

B.4 Composition diagnostics

  • 0.79 within one composition step versus top-1 accuracy of 0.64: conventional-branch mistakes were mostly neighboring Gd or Mn levels, not unrelated alloys.The learned branches were near 0.68 within one step while their top-1 accuracy stayed below 0.30, with mistakes spread across the catalogue.Source: Figure 8 · p. 19, §B.4 · p. 19
  • The conventional branch was exact on Zn, Al, Ce, and Y, with errors in Gd, Mn, Nd, and Ca; learned branches under-predicted rare Nd and Ca and added Mn or Ca to absent-element alloys.Together, the diagnostics attribute the descriptor gap to concentration resolution rather than chemistry recognition.Source: Figure 9 · p. 19, §B.4 · p. 19

B.5 Process diagnostics

Process diagnostics show that both temperature and velocity predictions saturate at the high end. For velocity, compression of fast conditions in the projected embedding explains the flattening and the resulting pull toward middle-range predictions.

B.5 Process diagnostics

  • Above approximately 400 °C, both temperature heads saturate, although the joint-grid GP’s latent intervals cover the diagonal on most held-out conditions.Both heads track the diagonal below that range.Source: §B.5 · p. 20
  • The GNN velocity response is sigmoidal and saturates at the fast end, while the conventional-branch parity view shows tight low-speed predictions and high-speed undershoot.The conventional response and parity views repeat the corresponding GNN analyses.Source: §B.5 · p. 20, Figure 13 · p. 21
  • Both velocity branches rise with speed and flatten at the fast end, making the fastest settings barely distinguishable in the descriptor whichever head reads it.The conventional projection is less well behaved because an extreme low-velocity cluster near −3 dominates it, but it shows the same saturation.Source: §B.5 · p. 20, Figure 12 · p. 21
  • Slow conditions spread across the 2-D projection while fast conditions compress into a narrow band, producing a sigmoidal response and predictions pulled toward mid-range speeds.Figure 14 shows the embedding from which the 1-D response curves are read.Source: §B.5 · p. 20, Figure 14 · p. 21

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