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Physics-based prediction, uncertainty quantification and decision-making for IN718 crystallographic texture intensity across LPBF defocus regimes

Yisheng Lu, John Riris, Jie Song, Yao Fu, Jie Chen

arXiv:2609.18863v1cs.LGcond-mat.mtrl-scics.CE

TL;DR

Reliable texture prediction matters because LPBF process conditions create direction-dependent crystallographic texture, while black-box models may not transfer across regimes or distinguish weak data support from physics invalidity. This study combines a process-to-melt-pool model with a physics-anchored texture model, residual learning, and separate applicability and validity decisions. The framework retained predictive capability in a withheld defocus condition where the unconstrained model did not, and withheld predictions where no evaluated model class performed adequately.

  • Problem

    Reliable prediction of ⟨001⟩ ∥ BD texture matters for linking LPBF process conditions to direction-dependent material response, and a reliable workflow must distinguish data support, physics validity, and uncertainty.

    Source: §1 · pp. 3, 5

  • Method

    A two-stage framework maps process variables to melt-pool geometry, then combines a conduction-inspired texture anchor with a random-forest residual model and separate applicability, physics-validity, and uncertainty mechanisms.

    Source: §1 · p. 5

  • Results

    The framework retained predictive capability in a withheld defocus condition where the unconstrained model did not, and issued no predictions in a regime where no evaluated model class performed adequately.

    Source: §1 · p. 6

  • Takeaways & Limitations

    The framework applies distinct withholding, attenuation, and prediction decisions to separately built conditions without adjustment to its fitted parameters or gate thresholds.

    Source: §1 · p. 6

    The reported 100% coverage at +80 mm is based on 42 observations under one regime shift, and conformal coverage is not guaranteed under arbitrary shifts or exchangeability violations.

    Source: §4.5 · p. 37

Abstract

from arXiv · show

Reliable prediction of crystallographic texture in laser powder bed fusion is critical for linking process conditions with anisotropic response and for qualification. However, black-box models may fail under shift and cannot distinguish weak data support from loss of physical validity. This study develops a two-stage physics-based model for <001> || BD (build direction) texture in Inconel 718. Stage 1 maps process variables to melting mode and melt pool geometry. Stage 2 predicts texture by combining an empirical physics model with a random-forest residual model. A k-nearest-neighbor weight attenuates residual corrections for poorly supported queries, while a study-specific areal beam-power-density criterion withholds predictions outside the adopted conduction envelope. Conformal intervals are evaluated on the retained physics-valid set, and SHAP and Sobol analyses assess residual sensitivity. Under a controlled leave-one-defocus-out evaluation, the physics anchor achieved R^2 = 0.778, against -0.001 for the black-box model and 0.750 for the gated hybrid. Under leave-one-group-out cross-validation, the gated hybrid reached R^2 = 0.592 against 0.538 for the black-box model. Retained-set coverage was 92.9% at a mean full width of 3.65 multiples of a uniform distribution (MUD) under grouped cross-validation and 100% at a width of 3.21 MUD under transfer to a withheld +80 mm defocus regime. An illustrative mapping produced a retained BD elastic-modulus span of 127-187 GPa. On nine conditions from a separately built sample set, the framework withheld three, attenuated three, and matched the measured ordering for the rest. Separating data applicability, physics validity, and predictive uncertainty into distinct decisions lets the framework transfer where an unconstrained model does not, and withhold predictions where no model class performs adequately.

1. Introduction

LPBF process conditions shape melt-pool evolution and texture, but reliable prediction across unseen process regimes requires separating data support, physics validity, and uncertainty. This study introduces a two-stage physics-anchored framework and evaluates its transfer and withholding behavior.

1. Introduction

  • Texture links process design to direction-dependent material response, but its formation depends on a multicycle process-to-melt-pool-to-solidification chain.The study adopts a conduction-dominated processing envelope rather than treating high texture under any melting state as equally desirable; black-box interpolation performance alone does not establish transfer to unseen regimes.Source: §1 · pp. 3–5
  • The framework separates residual applicability, physics-domain validity, and predictive uncertainty rather than collapsing them into one confidence measure.Intervals are calibrated through grouped cross-validation and reported only for retained predictions.Source: §1 · pp. 5–6
  • Stage 1 maps process variables to melting mode and melt-pool geometry, while Stage 2 combines a conduction-inspired anchor with a random-forest residual model.A k-nearest-neighbor distance attenuates residual corrections as data support weakens; a separate areal beam-power-density criterion withholds predictions outside the adopted physics-validity envelope.Source: §1 · p. 5
  • Evaluation excludes complete experimental groups and defocus levels from fitting and compares literature-derived model forms under the same protocol.The evaluation is designed to assess transfer across experimental groups and process regimes.Source: §1 · p. 6
  • The framework retained predictive capability in a withheld defocus condition where the unconstrained model did not, and withheld predictions in a regime where no evaluated model class performed adequately.On a separately built set, it applied the same distinction without adjustment by withholding, attenuating, or issuing predictions according to its criteria.Source: §1 · p. 6

2. Experimental setups and datasets

The study builds linked process-to-melt-pool and process-to-texture datasets, with EBSD observations organized into nine experimental groups. Its texture target is a point-fraction-based measure of ⟨001⟩ alignment with the build direction, and the groups support group-level validation.

2. Experimental setups and datasets

  • IN718 specimens were built with a meandering scan strategy and 90° inter-layer rotation, and EBSD texture measurements came from sections oriented with their observation-plane normal along BD.Texture scans used a 1.2–2 µm step size, with indexed points forming the measured target.Source: §2 · pp. 7–9
  • Stage 1 spans 372 process conditions, including 345 successful tracks used for melting-mode and geometry modeling; Stage 2 contains 278 EBSD observations across nine experimental groups.Stage-1 printability classification uses all 372 conditions, while melting-mode classification and geometry regression use the successful conditions.Source: §2 · pp. 7–8
  • Stage-1 models provide predicted melt-pool depth and width as Stage-2 inputs; measured Stage-1 geometry labels are not used directly for Stage 2.Fourteen Stage-2 observations fall outside the Stage-1 hatch-spacing range and are flagged as hatch-range extrapolations.Source: §2 · p. 8
  • The normalized texture target e001 is the fraction of indexed orientations within 15° of ⟨001⟩ ∥ BD divided by the 10.21% random-texture reference fraction.It is expressed in MUD, where 1 represents random texture and values above 1 indicate enrichment; it is based on measured EBSD orientations, not pole-figure maxima.Source: §2 · p. 9, Figure 1 · p. 10
  • LOGO validation holds out experimental groups, although some process vectors occur in two groups and can therefore appear in both training and test data.The Stage-2 dataset has 269 unique process vectors among 278 observations.Source: §2 · pp. 7, 10

3. Physics-based machine learning and statistical analysis

This section describes a two-stage framework that maps process conditions through melt-pool geometry to texture, while treating residual support, physics validity, and uncertainty as separate decisions. It also specifies grouped validation and model-interpretation analyses.

3.1 Overall physics-based modeling framework

  • Stage-1 maps process variables to printability, melting mode, and melt-pool geometry, whose predicted depth and width serve as Stage-2 mediators.The bridge uses a balanced RF printability classifier, XGBoost mode routing, CatBoost CM geometry regression, and GPR KM geometry regression.Source: §3.1 · p. 11, §3.2 · p. 13

3.4 roup- V conformal uncertainty quantification and physics-domain abstention

  • Grouped conformal calibration provides empirical 90% intervals for retained predictions, while a separate qPD criterion withholds both prediction and interval outside the adopted anchor-validity envelope.The study-specific threshold is distinct from the residual-support weight; coverage and width are reported only for retained cases, not as an unconditional guarantee.Source: §3.1 · p. 11, §3.4 · pp. 19–21

3.2 Stage-1 process-to-melt-pool bridge

  • Grouped-CV depth RMSEs were 0.021 mm for CM and 0.091 mm for KM, while width RMSEs were 0.041 mm for CM and 0.081 mm for KM.Depth parity is emphasized because predicted depth enters the Stage-2 greybox directly; width enters only the residual model.Source: §3.2 · p. 15

3.3 Stage-2 physics-anchored residual model and applicability weighting

  • Stage-2 combines a low-capacity, conduction-inspired empirical anchor in scan speed, power, and predicted depth with an RF model of residual departures.The residual model captures dependencies absent from the anchor, including hatch spacing, focus offset, predicted width, and nonlinear interactions; a kNN weight attenuates corrections as support weakens, returning toward the anchor with distance.Source: §3.3 · pp. 17–18

3.5 Validation protocol and statistical analysis

  • Primary Stage-2 LOGO validation withholds one of nine experimental groups at a time and evaluates the mapping conditional on a frozen Stage-1 surrogate.All 278 observations had measured targets, and pooled out-of-fold metrics are sample-weighted aggregates rather than unweighted group means.Source: §3.5 · pp. 21–23
  • The +80 mm and focus-zero defocus tests probe different conditions: weak residual support within the adopted envelope versus qPD above the threshold, where predictions are withheld.The +80 mm test was a controlled withheld-defocus evaluation, not independent external validation; all focus-zero queries exceeded the threshold.Source: §3.5 · p. 22
  • Bootstrap exponent intervals are conditional on predicted depth, while SHAP and Sobol agreement reflects a shared synthetic independent-input reference rather than independent validation.The nine-group bootstrap describes resampling stability, not complete workflow uncertainty or a causal scaling law.Source: §3.5 · p. 24

4. esults and discussion

The gated hybrid improved grouped performance over the black-box model, while the +80 mm holdout showed transfer near the physics anchor and focus-zero prompted abstention. Gate ablations, conformal intervals, and residual sensitivity analyses clarify the framework’s trade-offs and scope.

4.1 rouped generalization performance

  • R²=0.592 for the gated hybrid, versus 0.538 for the black-box RF, 0.564 for the ungated hybrid, and 0.287 for the greybox anchor under LOGO.The gated model also reduced MAE and RMSE to 0.856 and 1.156 MUD, from 0.933 and 1.229 MUD for the black-box model.Source: §4.1 · p. 25, Table 3 · p. 26

4.2 eliability under withheld-defocus regime shift

  • At +80 mm, the gated hybrid reached R²=0.750, near the greybox anchor’s 0.778 and above the black-box RF’s −0.001; focus-zero predictions were all withheld.At focus-zero, the three models’ R² values were −0.298, −1.092, and −0.378 for the greybox, black-box RF, and gated hybrid, respectively; all 54 queries exceeded the validity threshold.Source: §4.2 · pp. 28–29, Figure 5 · p. 28
  • The +80 mm evaluation was controlled rather than independent external validation, and one KM-routed observation among 278 Stage-2 cases did not support comparing defect-free CM texture with defect-associated KM texture.Post hoc literature-derived baselines remained below the physics anchor at +80 mm, but published study accuracies were not like-for-like rankings.Source: §4.2 · pp. 29–30

4.3 reybox scaling relation and depth-mediator ablation

  • Removing model-derived depth reduced greybox R² from 0.287 to 0.059 under LOGO and from 0.778 to −0.116 at +80 mm, establishing predictive relevance but not causality.For fixed layer thickness, log EV and a single multiplicative hatch term span the same column space once P and V are included; these additions slightly improved LOGO but reduced +80 mm transfer.Source: §4.3 · pp. 32–33

4.4 Applicability weighting and gate ablation

  • The soft gate achieved R²=0.592 under LOGO and 0.750 at +80 mm, versus 0.564 and 0.199 for the ungated hybrid.At +80 mm, the soft gate attenuated the residual by 80.5% on average; the hard gate recovered anchor performance at R²=0.778 but reduced LOGO performance to 0.530.Source: §4.4 · pp. 33–34, Table 6 · p. 34

4.5 roup- V conformal uncertainty and physics-validity abstention

  • Under LOGO, intervals achieved 92.9% empirical coverage on the retained set at a mean full width of 3.65 MUD, 34% narrower than the 5.57-MUD regime-specific null width.At +80 mm, all 42 observations were retained and gated intervals achieved 100% coverage at a mean full width of 3.21 MUD. At focus-zero, all 54 observations were withheld; black-box intervals covered 53.7%.Source: §4.5 · p. 36
  • The 100% +80 mm coverage came from 42 observations under a specific shift, not a theoretical guarantee under arbitrary shifts; the physics-validity threshold was study-specific.Coverage is empirical on retained sets and should be read together with retention.Source: §4.5 · pp. 35, 37

4.6 Process-level interpretation of the learned residual

  • Residual SHAP attributed 37% to scan speed, 31% to hatch spacing, 27% to focus offset, and 4% to power, while Sobol ranked hatch spacing and scan speed highest.The hatch interaction indicator ST-S1 was 0.111, the largest among the four variables; mediator inputs mean sensitivities do not separate direct from Stage-1-mediated effects.Source: §4.6 · pp. 37–38

5. Illustrative application to build-direction elastic modulus

This section maps retained texture predictions to build-direction modulus and checks the assumed texture–stiffness association in tensile tests at room temperature and 650 °C. A separately built set illustrates the framework’s withholding and attenuation decisions, while the modulus mapping remains literature-informed.

5.1 Texture-to-modulus mapping and application

  • The bounded, literature-informed mapping treats build-direction Young’s modulus as a monotone nonincreasing function of predicted texture intensity, clipped to 125–195 GPa.Lower build-direction modulus is not claimed to be desirable for every application.Source: §5.1 · pp. 40–41
  • The 224 retained LOGO predictions mapped to build-direction moduli of approximately 127–187 GPa, with stronger predicted ⟨001⟩ ∥ BD texture corresponding to lower modulus.The empirical 90% texture intervals were propagated through the mapping; their uncertainty does not include uncertainty in the mapping form or material constants.Source: §5.1 · p. 41, Figure 9 · p. 44
  • The framework withheld three of nine separate-build conditions, attenuated three corrections to about 12%, and matched measured enrichment ordering across the six conditions receiving predictions or attenuation.For the three issued predictions, mean absolute error was 1.02 MUD; all three mapped-modulus intervals contained the measured value.Source: §5.1 · p. 42, Table 8 · p. 43

5.2 irectional response at service temperature

  • At room temperature and 650 °C, apparent build-direction stiffness ranked inversely with enrichment (Spearman correlations −0.85 and −0.78), while room-temperature proof stress did not follow enrichment.The tests used the same specimens for texture and mechanical response; apparent stiffness is interpreted as a relative trend rather than an elastic modulus.Source: §5.2 · pp. 45–46, Table 9 · p. 45
  • Apparent tensile stiffness includes machine and fixture compliance, and observed variation may also reflect unmeasured porosity or grip conditions.The authors characterize it as a semi-quantitative measure of relative trends among processing conditions.Source: §5.2 · p. 46

6. onclusions

The conclusion reports improved grouped generalization for the gated hybrid and strong transfer by the empirical anchor in the withheld +80 mm regime. It emphasizes separate decisions for residual applicability, physics validity, and uncertainty, while identifying broader validation needs.

6. onclusions

  • The framework combines a frozen Stage-1 melt-pool surrogate with a Stage-2 conduction-inspired anchor, residual learning, applicability attenuation, physics-validity abstention, and retained-set uncertainty quantification.Its use distinguishes data support, physics validity, and uncertainty rather than combining them into one confidence measure.Source: §6 · p. 47
  • Under LOGO grouped generalization, the gated hybrid reached R2 of 0.592 versus 0.538 for the black-box RF; for withheld +80 mm, the greybox and gated hybrid reached R2=0.778 and 0.750, versus −0.001 for the black-box RF.At focus-zero, all 54 queries exceeded the adopted validity threshold and predictions and intervals were withheld.Source: §6 · p. 47
  • The conclusion calls for validation on additional machines and extensometer-measured strain, alongside matched melt-pool, defect, and mechanical-property data.The reported retained-set interval coverage is not a general coverage guarantee under regime shift.Source: §6 · p. 47

ediT authorship contribution statement

The contribution statement lists roles spanning research design, analysis, data work, writing, supervision, and project support.

ediT authorship contribution statement

  • Listed contributions include conceptualization, methodology, software, formal analysis, investigation, data curation, resources, supervision, writing, visualization, funding acquisition, and project administration.The passages assign these roles across the named contributors.Source: ediT authorship contribution statement · p. 48

ata availability

Processed data and analysis code are available from the corresponding author upon reasonable request, with original EBSD materials subject to data-owner approval.

ata availability

  • Processed data, analysis code, finalized targets, frozen Stage-1 predictions, saved Stage-2 outputs, uncertainty and mechanism analyses, and scripts are available from the corresponding author upon reasonable request.Original EBSD orientation maps and crystallographic-processing information are available on the same basis, subject to data-owner approval.Source: ata availability · pp. 48–49

Supplementary Information for Physics-based Prediction, uncertainty quantification and decision-making for IN718 crystallographic texture intensity across LPBF defocus regimes

The supplementary analyses specify how residual-model interpretation was sampled and how the deployed applicability gate behaves under sensitivity sweeps. They also qualify interpretation as distribution-dependent and report greater gate sensitivity under withheld-regime transfer than grouped generalization.

S1. Sampling and surrogate settings for the residual-model interpretation

  • SHAP and Sobol analyses sampled four controllable process variables and used deterministic surrogates for the Stage-1 melt-pool mediators before evaluating the six-feature residual model.The mediator surrogates approximated frozen Stage-1 outputs and were fitted to the 278 Stage-2 observations, without independent-sample evaluation.Source: additive explanations (SHAP) and Sobol… · p. 56, S1. Sampling and surrogate settings… · p. 56, Table S1 · p. 57
  • The Sobol indices describe the fitted residual forward mapping under a synthetic independent-input distribution, not a variance decomposition of the experimental design.The SHAP attribution surrogate was not independently evaluated, and agreement between SHAP and Sobol reflects a shared reference distribution rather than independent validation.Source: additive explanations (SHAP) and Sobol… · pp. 57–58

S2. Applicability-gate sensitivity sweep

  • The gate sweep varied one quantity at a time, refitting within each training partition so held-out texture targets did not contribute to gate calibration.The deployed k = 5 and 95th-percentile settings were inherited from the canonical implementation, fixed before the sweep, and not selected using it.Source: S2. Applicability-gate sensitivity sweep · pp. 59–60
  • Increasing k from 5 to 15 or the reference percentile from 95 to 99 was associated with lower +80 mm R², from 0.750 to 0.656 and 0.606, respectively.Grouped generalization varied by less than 0.02 in R² across the swept settings; the deployed configuration remained k = 5 and percentile 95.Source: S2. Applicability-gate sensitivity sweep · p. 59, Table S3 · p. 59
  • The sweep tested no neighborhood size below k = 3 because smaller neighborhoods make distance estimates increasingly sensitive to individual nearest neighbors.At k = 1, normalized distance depends entirely on one training observation and loses its intended local data-density interpretation.Source: S2. Applicability-gate sensitivity sweep · p. 60

S3. Texture-target reference fraction

The adopted 10.21% random-texture reference fraction is consistent with an analytical and independent Monte Carlo estimate. The supplement also maps the manuscript group labels to archive identifiers and explains why the acquisition set begins at OR-4.

S3. Texture-target reference fraction

  • 10.222% is the analytical random-orientation fraction within 15° of a symmetry-equivalent ⟨001⟩ direction, and Monte Carlo gave 10.2218% ± 0.0086 percentage points.The Monte Carlo estimate used 5 × 10⁷ Haar-uniform random rotations and agreed with the analytical expectation to 0.0005 percentage points.Source: S3. Texture-target reference fraction · p. 61
  • The workflow retained its adopted 10.21% reference value; replacing it with 10.222% would rescale e₀₀₁ by 0.9988 and shift the observed maximum from 7.965 to 7.955 MUD.The archived value was retained for consistency with the finalized target table and downstream results.Source: S3. Texture-target reference fraction · p. 61

S4. Experimental group labeling

  • The manuscript labels G1–G9 and the archive acquisition identifiers refer to the same nine groups and 278 observations.Identifiers begin at OR-4 because the texture campaign sampled a conduction-focused subset; OR-1 to OR-3 were predominantly negative-focus and keyhole-mode conditions not advanced to EBSD characterization.Source: S4. Experimental group labeling · p. 62, Table S4 · p. 62

S5. omparison with representative texture-prediction frameworks

The supplement contextualizes representative LPBF texture-prediction studies by their reported scope rather than ranking their accuracy. It also reports MAPE for the present point predictors while cautioning that the metric should be read alongside scale-preserving errors.

S5. omparison with representative texture-prediction frameworks

  • Reported accuracies from prior LPBF texture-prediction studies are not directly comparable because target definitions, datasets, and validation designs differ.Table S5 summarizes what each study reported rather than placing studies on a common accuracy scale.Source: S5. omparison with representative… · p. 63, Table S5 · p. 64
  • Table S6 reports MAPE for four point predictors under three evaluation settings, interpreted alongside Table 3 MAE and RMSE because MAPE weights lower e₀₀₁ observations more.Focus-zero MAPE values are diagnostic because no operational prediction was issued for that subset.Source: Table S6 · p. 65

S6. Protocol-matched baselines from literature-derived model forms

The supplementary baselines apply literature-derived model forms to the present IN718 dataset under protocol-matched evaluations, as diagnostic benchmarks rather than reproductions or model-selection tools. Their focus-zero comparisons are diagnostic because the proposed framework withholds those predictions.

S6. Protocol-matched baselines from literature-derived model forms

  • Literature-derived model forms were evaluated on the present IN718 dataset under the study protocols, as post hoc diagnostic benchmarks rather than reproduced source-study results or model-selection inputs.Material, target definition, and validation design differ from the source studies; data-dependent tuning was confined to outer-training partitions.Source: S6. Protocol-matched baselines from… · p. 66, Table S7 · p. 67
  • The reduced geometric surrogate retains a single-pool boundary-orientation calculation and omits the full mechanistic model’s multi-track and multi-layer growth selection.It is not a reproduction of the full mechanistic model.Source: Table S7 · p. 67
  • Unlike literature-derived and internal point-prediction baselines, the proposed framework withholds all focus-zero predictions, so its negative diagnostic coefficient is not an operational prediction failure.The focus-zero column is reported for diagnostic purposes only.Source: S6. Protocol-matched baselines from… · pp. 67–68
  • Across three cost-complexity pruning implementations, the defocus-aware tree remained below the physics anchor’s +80 mm R² of 0.778.The canonical implementation used the exact training-partition pruning path and selected the subtree with minimum mean ten-fold validation error; alternatives used pre-specified alpha grids.Source: Table S8 · p. 68
  • Table S8 compares +80 mm R² across pruning implementations, while Table S9’s focus-zero treatment distinguishes diagnostic predictions from withheld framework outputs.Table S8 describes exact pruning-path selection versus pre-specified alpha grids; the supplied focus-zero comparison identifies prediction versus withholding treatment.Source: Table S8 · p. 68, S6. Protocol-matched baselines from… · p. 68

S7. eproducibility

  • The supplementary analyses used deterministic settings, with gate sweeps refitted within evaluation partitions and literature-derived baselines refitted with pruning selection confined to outer-training partitions.The archive includes scripts, intermediate files, and per-observation predictions for the predictors and protocols.Source: S7. eproducibility · p. 69

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