Nature Communications · 2026Open AccessDOI 10.1038/s41467-026-77119-6

Knowledge-informed graph attention networks enable defect-free alloy design for laser additive manufacturing

A machine-learning framework that unites a physical-metallurgy knowledge graph with Bayesian uncertainty quantification — designing two new crack-free 3D-printable alloys from small experimental datasets.

Jiabo Fu^†^1,6, Hao Yu^†^1,6, Chenchong Wang^✉¹, Lingyu Wang¹, Zhongji Sun^✉², Jinguo Li³, Sybrand van der Zwaag⁴, Dierk Raabe⁵, Wei Xu^✉¹

¹ State Key Laboratory of Digital Steel, Northeastern University, Shenyang, China

² Institute of Materials Research and Engineering (IMRE), A*STAR, Singapore

³ Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China

⁴ Novel Aerospace Materials Group, TU Delft, the Netherlands

⁵ Max Planck Institute for Sustainable Materials, Düsseldorf, Germany

† These authors contributed equally · ✉ Corresponding: wangchenchong@ral.neu.edu.cn, zhongji-sun@outlook.com, xuwei@ral.neu.edu.cn

Article Supplement Source data Code

New alloys designed

KG-AMS (Ni superalloy) & KG-AMAA (Al alloy)

0.037%

Lowest defect level

KG-AMS pore area fraction — crack-free

1,307 MPa

Ultimate tensile strength

KG-AMS at room temperature, 22.2% elongation

142 / 163

Samples in Ni / Al datasets

Small-data regime: 15 features, 12 alloying elements

Received 23 September 2025 · Accepted 7 August 2026

01Overview

One framework, two new printable alloys

The study introduces UQ-KGAT — an Uncertainty-Quantified, Knowledge-informed Graph Attention Network — coupled with NSGA-II for inverse design of composition and process, and proves it by printing two entirely new alloys without cracks.

The problem

Alloys built by laser 3D printing crack and form pores; designing printable alloys needs huge, costly datasets that conventional ML depends on.

The idea

Encode physical-metallurgy knowledge as a graph, let a graph attention network learn from it, and quantify both statistical and model uncertainty.

The proof

Two brand-new crack-free alloys — KG-AMS Ni superalloy (1.3 GPa strength) and KG-AMAA Al alloy — designed, printed and validated.

Abstract

View at Nature.com

Machine learning offers a promising approach to design high-performance alloys for laser additive manufacturing, by bypassing convoluted physical models and identifying correlations among composition, processing, microcracks/porosity and properties. However, conventional machine learning methods face limitations, e.g., overfitting or unreasonable design results, due to reliance on large, high-quality datasets. Here, we introduce a generic framework operable with smaller experimental datasets, by integrating knowledge-informed graph modeling alongside data uncertainty quantification. The generic physical-metallurgy knowledge and the stochasticity of experimental defect distributions from produced material are rationally balanced. To validate the approach, we detail the development of a new defect-free Ni superalloy possessing excellent laser printability, thermal stability, and high mechanical strength. Mechanism mining revealed a possible origin for this performance, which was confirmed by atom probe tomography. Subsequently, we developed a new laser-printable aluminum alloy through the same approach, highlighting the framework's potential to accelerate next-generation alloy design for additive manufacturing.

Graph neural networksKnowledge graphUncertainty quantificationL-PBFL-DEDNSGA-IINi superalloyAl alloy

02The challenge

Why designing printable alloys is so hard

Laser additive manufacturing promises complex geometries and tailored microstructures — yet powders developed for casting or forging crack, oxidize and fail when laser-printed. Four compounding difficulties stand in the way.

Cracks & porosity are stochastic

Defects in AM parts show heterogeneous, random spatial distributions. Deterministic ML models built on 2D optical microscopy struggle to capture bulk defect levels reliably — a fundamental mismatch between model and reality.

Domain knowledge resists encoding

Materials behavior is governed by nonlinear, partially empirical principles. Qualitative guidelines and semi-quantitative models don't fit conventional numerical ML pipelines — so most studies optimize process parameters only.

Small, noisy datasets cause overfitting

Experimental alloy datasets are small and imperfect. Purely data-driven models overfit, extrapolate poorly, and generate unreliable inverse-design results — sometimes proposing alloys that cannot be printed at all.

Printability vs performance trade-off

High-strength Ni superalloys crack during printing; printable ones sacrifice strength. Breaking this trade-off requires co-optimizing composition AND process — a vast search space spanning 12+ elements and wide laser parameters.

The requirements: a framework that (1) assembles heterogeneous data — numerical, qualitative, empirical — to mitigate data scarcity and embed domain knowledge, and (2) reconciles statistical uncertainty (defect stochasticity) with model uncertainty (mean-field approximations) to stay reliable under real-world AM process variability.

03Framework

UQ-KGAT: physics as a graph, uncertainty as a first-class output

Two stages: (i) build a physical-metallurgy knowledge graph and train an uncertainty-quantified graph attention network; (ii) hand the model to NSGA-II for inverse, dual-objective design of composition and laser process.

Workflow of the UQ-KGAT framework: knowledge graph construction, model architecture and NSGA-II design loop — Fig. 1 | Workflow of additive manufacturable Ni superalloy design using UQ-KGAT and NSGA-II. a Construction of a physical-metallurgy-knowledge-informed graph, where nodes represent quantitative information (composition, process, physical-metallurgy parameters, property) and directed edges encode hierarchical qualitative relationships. b The UQ-KGAT model predicts defect level and its uncertainty per sample. c Coupling with the NSGA-II algorithm for inverse composition-process design. d Collaborative design results across the design space.

Knowledge-informed graph

Nodes hold quantitative data — composition, process, thermodynamic and solidification variables, hardness. Directed edges encode qualitative physical-metallurgy relationships, e.g. composition → γ′ driving force, so the model learns physics-aware attention instead of blind correlations.

Graph attention network

A GAT convolves features over the graph with learnable attention weights (LeakyReLU scoring + SoftMax normalization + multi-head averaging), prioritizing physically meaningful feature interactions even with limited training samples.

Heteroscedastic regression

Statistical (aleatoric) uncertainty is learned from data as a loss-attenuation factor — the model automatically predicts higher variance for noisy samples, down-weighting their influence during training.

Monte Carlo dropout

Model (epistemic) uncertainty is estimated by keeping dropout active at inference and measuring prediction variance across stochastic forward passes — a Bayesian view of what the model doesn't know.

NSGA-II inverse design

The UQ-KGAT serves as objective function inside a dual-objective genetic algorithm that co-optimizes defect level AND uncertainty over composition-process space — 13 decision variables, population 50, 1,500 generations.

Secondary-feature surrogates

Thermodynamic variables (Thermo-Calc TCNI12/MOBNI6), FEM solidification kinetics and hardness are predicted by fast surrogate models inside the design loop, slashing computational cost of each generation.

Ni dataset

142 samples · 15 features

5 superalloys, 12 elements, L-DED

Laser process window

600–1,600 W · 4–14 mm s⁻¹

hatch 1.2–2.0 mm, layer 0.6–0.7 mm

Target

Defect area fraction (%)

porosity + microcracks via OM image analysis

Evaluation

20 random 4:1 splits

R² 76.7% · MAE 0.238% (average)

04Interactive results

Explore the data behind the discovery

Every chart below is rendered live from the paper's official Source Data file — hover points, toggle models and compare model families yourself.

Defect prediction across the Ni-superalloy dataset

R² 76.7% avgMAE 0.238%

142 L-DED samples · 20 random 4:1 train/test splits · error bars show predicted total uncertainty (statistical + model)

The diagonal is the ideal y = x line. Statistical uncertainty dominates over model uncertainty — stochastic defect distribution, not model architecture, is the primary barrier to accurate defect prediction (Supplementary Fig. 6).

Inverse design benchmark — Pareto fronts by model family

Toggle models to compare. Lower-left = better: low defects AND low uncertainty. Colors follow the paper's Fig. 2b–g; the dashed line marks the best defect level found in the dataset (0.05%).

UQ-KGAT finds the optimal Ni solution KG-AMS with markedly lower defect levels and uncertainty. Models without physical parameters generally shift to an inferior domain — higher uncertainty or defect fraction. Reducing training data size barely hurts UQ-KGAT (Suppl. Fig. 7), showing knowledge-graph integration boosts extrapolation.

Thermodynamic crack-susceptibility map

Freezing-range factor vs strain-age-cracking (SAC) factor, colored by γ′ content at 900 °C (log y-axis). Star = KG-AMS.

KG-AMS shows the lowest susceptibility to BOTH hot cracking (FR) and cold cracking (SAC) — outperforming the four ML-designed alloys and all commercial references — while retaining a relatively high γ′ fraction at service temperature.

Figure 2 - design results and computational validation — Fig. 2 | Design results of additive manufacturable Ni superalloys and computational validation. a Prediction of defect area fractions for n = 142 samples (20 random 4:1 splits). b–g Pareto-front comparison across UQ-KGAT, UQ-CNN and UQ-ANN models with/without physical parameters. h Thermodynamic validation: γ′ content at 900 °C versus cracking criteria.

Figure 3 - experimental validation of KG-AMS — Fig. 3 | Experimental validation of the designed alloy KG-AMS. a Hardness–defect correlation map against 142 reference samples. b Predicted vs measured defect fractions for 18 parameter sets. c–f Optical micrographs under different laser parameters. g Predicted vs measured hardness. h–k SEM images of γ′ precipitates with size-distribution insets.

Figure 5 - extension to aluminum alloys — Fig. 5 | Extension of the UQ-KGAT framework to high-strength Al alloys. a Relative-density prediction for n = 163 samples. b Pareto design results with the optimal AI solution KG-AMAA. c–e Optical micrographs at different volumetric energy densities. f, g EBSD inverse pole figure maps. h KG-AMAA benchmarked against 163 reference AM-ed Al alloys.

05New alloys

Two alloys that did not exist before this study

Designed by UQ-KGAT + NSGA-II, gas-atomized into powder, laser-printed and fully validated — compositions, properties and processing windows below come straight from the paper's Tables 1–2 and experimental campaigns.

★KG-AMS

Ni-based superalloyL-DED · 1,500 W / 10 mm s⁻¹ optimumKnowledge Graph-based Additive Manufacturable Superalloy

Alloy composition — KG-AMS

Table 1

wt.%	Al	Co	Cr	Mo	Ta	Ti	W	C	B	Nb	Hf	Ni
Designed	6.31	14.59	5.06	0.25	1.56	0.14	2.25	0.21	0.01	2.1	0.006	Bal.
Actual (ICP-OES)	6.33	14.24	5.12	0.31	1.54	0.08	2.38	0.2	0.01	2.14	0.011	Bal.

Defect area fraction

0.037–0.133%

across 18 L-DED parameter sets

Hardness

391–417 HV

upper limit of printable range

γ′ phase content

47.7 ± 2.1%

vs 40.7% in printable references

γ′ size

87.4 ± 14.7 nm

thermal-history resistant

Lattice misfit

0.05–0.07%

vs 0.12% in cracked reference

Tensile strength

1,307 MPa / 22.2%

UTS / elongation, RT

Hot tensile

655 MPa / 7.5%

UTS / elongation, 900 °C

Creep rupture life

97.8 h

900 °C / 200 MPa

Why it works: mechanism mining (Integrated Gradients) flagged elements promoting γ′ formation (Nb) plus the thermodynamic variables — γ′ driving force and γ′ molar volume — as dominant factors. KG-AMS has a higher γ′ content (47.7%) than printable references (40.7%) while its compositionally stabilized γ/γ′ architecture keeps precipitation slow and uniform: minimal lattice misfit (0.05–0.07% vs 0.12% for the cracked reference) resists thermal-gradient destabilization during cyclic laser heating. Impurities: 100 ppm O, 20 ppm N, <10 ppm S. Powder D10/D50/D90 = 45.9 / 78.1 / 134.7 µm.

★KG-AMAA

High-strength aluminum alloyL-PBF · 350 W / 1,100 mm s⁻¹ optimumKnowledge Graph-based Additive Manufacturable Al Alloy

Alloy composition — KG-AMAA

Table 2

wt.%	Si	Fe	Cu	Mg	Sc	Zr	Mn	Zn	Ni	Al
Designed	4.41	0.2	2.63	0.11	1.08	0.001	0.47	0.4	0.25	Bal.
Actual (ICP-OES)	4.62	0.21	2.59	0.17	0.99	0.01	0.52	0.54	0.25	Bal.

Relative density

99.96 ± 0.02%

L-PBF, crack-free

Lowest porosity

0.03%

350 W / 1,100 mm s⁻¹

Hardness

128.3 ± 4.0 HV

outperforms 163 reference alloys

Melt-pool grains

3.9 ± 1.3 µm

cellular at boundaries

Columnar + cellular

12.7 ± 3.3 µm

melt pool interiors

Solidification interval

38.4 K

narrow → low hot-cracking

Predicted density

99.99%

exceeds dataset best 99.98%

Precipitates

~10 vol.%

strengthening potential

Why it works: thermodynamic analysis revealed favorable non-equilibrium solidification — primary Al₃Sc phases form during initial solidification and act as potent heterogeneous nucleation sites, refining the α-Al matrix to suppress epitaxial grain growth, residual stress and cracking. A narrow critical solidification interval (38.4 K) keeps hot-cracking susceptibility low, while ~10 vol.% of precipitates at lower temperatures provide strong precipitation strengthening. Powder D10/D50/D90 = 16.9 / 35.0 / 55.4 µm.

Figure 4 - APT and neutron diffraction of KG-AMS — Fig. 4 | Spatial distribution of γ′ precipitates, γ/γ′ elemental partitioning and lattice misfit in KG-AMS. a–d Uniform γ′ size distributions at 2.5, 5.0 and 7.5 mm build heights. e–j Atom probe tomography: Nb and Ta partition strongly to γ′ (k_γ/γ′ ≈ 10), Cr and Co to the γ matrix — nearly identical in bulk and substrate-adjacent regions despite divergent thermal histories. l, m Neutron diffraction confirms minimal, uniform lattice misfit (0.050% bulk vs 0.073% substrate-adjacent).

06Mechanism

Data-driven mechanism mining, experimentally confirmed

Integrated-Gradients sensitivity analysis on the UQ-KGAT model predicted that γ′ thermodynamics dominate KG-AMS's exceptional behavior. APT, neutron diffraction and mechanical testing then confirmed it.

Atom probe tomography

CAMECA LEAP 6000XR, UV pulsing at 200 kHz / 25 pJ, ~50 K. Nb and Ta partition to γ′ with coefficients ≈ 10; Cr and Co to the matrix — identical in bulk (7.5 mm) and substrate-adjacent (2.5 mm) regions despite cyclic vs rapid cooling thermal paths.

Neutron diffraction

ERNI time-of-flight diffractometer at the China Spallation Neutron Source. Rietveld fitting gives γ/γ′ lattice misfit of 0.050% (bulk) and 0.073% (substrate-adjacent) in KG-AMS — versus up to 0.12% with tensile residual stress in the cracked reference alloy AMS-mCB.

Tensile & creep

1,307 MPa UTS with 22.2% elongation at RT; 655 MPa / 7.5% at 900 °C. Creep rupture: 97.8 h at 900 °C/200 MPa and 70.7 h at 800 °C/400 MPa — outperforming existing printable Ni superalloys including AMSC-DB.

Thermal stability

Uniform γ′ (87.4 ± 14.7 nm) insensitive to laser power across the whole window — the crack-prone reference shows 44.8–129 nm heterogeneity. Slow precipitation and coarsening kinetics minimize misfit despite repeated precipitation/dissolution events.

The element-level agreement between model mechanism mining and atom-scale APT measurement is the key epistemic win: the knowledge graph did not just fit the data — it pointed to the physical origin (controlled γ′ precipitation thermodynamics and kinetics) that experiments then verified, providing a causal storyline for why KG-AMS can be both strong and crack-free.

07Methods

From powder to proof

Every claim in the paper is backed by a full experimental pipeline — here is the condensed version; the Supplement carries all 17 notes with complete details.

Powder & DED printing

Vacuum induction melting + argon gas atomization. Custom L-DED at IMR CAS: ytterbium fiber laser, ~3.0 mm beam, 7 g min⁻¹ powder feed, argon shield (<1,000 ppm O₂), 90° interlayer rotation. Matrix: 600–1,600 W, 4–14 mm s⁻¹, 1.2–2.0 mm hatch, 0.6–0.7 mm layers.

L-PBF printing (Al)

AmPro SP-160, 80 µm spot, flowing argon. Powder vacuum-dried at 120 °C for 2 h; 67° interlayer rotation. Screening: 250–390 W, 700–1,700 mm s⁻¹, 0.10 mm hatch, 30 µm layers — optimum at 350 W / 1,100 mm s⁻¹ (106.1 J mm⁻³).

Microstructure

Leica DM6 OM with ImageJ stereology for defect fractions (5 fields/sample); JSM-7800F SEM for γ′ (Obj./Total area); Oxford EBSD at 0.35 µm step; FEI Talos F200X TEM with twin-jet polishing at −30 °C; XRADIA 620 VERSA XCT at ~2 µm voxel for 3D porosity.

Mechanics & chemistry

ZD-HVZHT-10 Vickers (0.5 kg, 16 indents); RT tensile at 10⁻³ s⁻¹ (M6×φ3 bars, gauge 20 mm); F-25 creep frames at 800 °C/400 MPa and 900 °C/200 MPa; ICP-OES chemistry; CAMECA LEAP 6000XR APT; CSNS ERNI neutron diffraction with GSAS Rietveld fitting.

The model in equations

Attention (Eq. 5–6)

eᵢⱼ = LeakyReLU(aᵀ[Whᵢ ∥ Whⱼ])

αᵢⱼ = softmaxⱼ(eᵢⱼ)

multi-head output averaged over K heads (Eq. 8)

Heteroscedastic loss (Eq. 10)

L = Σᵢ (1/2σ̂ᵢ²)‖yᵢ − ŷᵢ‖² + ½ log σ̂ᵢ²

model uncertainty = variance across N MC-dropout passes (Eq. 9)

Read the full Supplementary Information (49 pages, 17 notes)

08Resources

Everything is open — dig deeper

The paper, supplement, source data, datasets and code are all publicly available. Start with any card below.

The article

Open-access full text at Nature Communications, including all methods, references and figure captions.

nature.com/articles/s41467-026-77119-6

Supplementary Information

49 pages · 17 notes · 28 figures · 7 tables — model details, crack-susceptibility analysis, creep data, KG-AMAA design walkthrough and more.

Download PDF (MOESM1)

Source Data

23 Excel sheets — the raw numbers behind Figs. 2–5 and 18 supplementary figures. Every chart on this site is rendered from this file.

Download XLSX (MOESM3)

Figshare deposit

The dataset generated in this study is additionally deposited on Figshare (ref. 69 in the paper).

figshare.com

FuJiabo-NEU/ML-AM-alloy-design

Apache-2.0 · Python 3.9 · PyTorch 1.13.1 + CUDA 11.7 · geatpy

Clone from GitHub

UQ-KGAT model.py

552 lines · GAT definition, heteroscedastic training loop, Monte-Carlo dropout uncertainty, graph dataset construction from the knowledge-graph adjacency matrix.

Sorting algorithm NSGA-II.py

503 lines · loads pretrained surrogate models, chains them into the prediction pipeline, runs NSGA-II over 13 decision variables for 1,500 generations (population 50).

Normalized datasets

Ni_normalized_data.xlsx and Al_normalized_data.xlsx — z-score normalized inputs ready for training, mirroring the paper's preprocessing.

GPU strongly recommended — Monte-Carlo dropout sampling and the genetic algorithm are expensive. Scripts auto-detect CUDA and fall back to CPU.

Cite this work

Fu, J., Yu, H., Wang, C. et al. Knowledge-informed graph attention networks enable defect-free alloy design for laser additive manufacturing. Nat. Commun. (2026). https://doi.org/10.1038/s41467-026-77119-6