Data-Driven Crystal Plasticity Modelling

• Data-driven crystal plasticity modelling is a computational approach that uses experimental and simulation data to refine traditional crystal plasticity models.
• It employs surrogate models such as ANN, LSTM, and operator learning to predict orientation evolution, stress fields, and homogenized responses while retaining microstructural sensitivity.
• The approach integrates rigorous calibration and uncertainty quantification, leveraging lower-scale data like DDD and DFT to enhance constitutive model fidelity.

Searching arXiv for recent and foundational papers on data-driven crystal plasticity modelling. arXiv search query: data-driven crystal plasticity modelling surrogate calibration uncertainty quantification orientation evolution Searching arXiv for "data-driven crystal plasticity". In the literature surveyed here, data-driven crystal plasticity modelling denotes a family of approaches in which crystal plasticity is accelerated, constrained, calibrated, or reformulated using simulation and experimental data rather than only through manual constitutive fitting. The resulting workflows range from supervised surrogates for orientation evolution, local stress fields, and homogenized stress–strain response, to constitutive discovery from discrete dislocation dynamics (DDD), first-principles-informed parameter transfer, uncertainty quantification, and direct stress reconstruction from multimodal experiments (Saidi et al., 2021, He et al., 2024, Pribe et al., 9 Mar 2026). Across these variants, the common objective is to retain microstructure sensitivity while reducing the cost, ambiguity, or limited observability of conventional crystal plasticity.

1. Problem classes and data sources

The field spans several distinct, but related, targets. One class learns orientation evolution during deformation. For FCC aluminum under rolling, the task is prediction of the orientation evolution path (OEP) of each crystal in Bunge Euler space from $0\%$ to $30\%$ reduction (Saidi et al., 2021). A second class learns local field evolution, such as the tensile-direction stress field in $32\times 32$ oligocrystals during plane-strain uniaxial tension (Frankel et al., 2019), or voxelwise 3D orientation updates in EVPFFT-generated copper microstructures under uniaxial tension (Pandey et al., 2020). A third class targets homogenized response, including mean-field stress–strain curves for polycrystal RVEs (He et al., 2024) and texture-dependent convex macroscopic yield functions suitable for FE$^2$-type use (Fuhg et al., 2022). A fourth class addresses inverse problems, such as parameter sensitivity, calibration, and uncertainty quantification for CPFE or spectral CP models (Dorward et al., 2023, Kumar et al., 24 May 2025, Pribe et al., 9 Mar 2026). A fifth class uses lower-scale data to construct constitutive laws directly, notably from DDD (Akhondzadeh et al., 2020, Julian et al., 5 Sep 2025), or from density functional theory (DFT) and Peierls–Nabarro analysis (Shimanek et al., 2020).

Modelling target	Data source	Representative papers
Orientation evolution	Taylor model, EVPFFT, EBSD	(Saidi et al., 2021, Pandey et al., 2020)
Local stress fields	CP simulations on oligocrystals	(Frankel et al., 2019)
Homogenized response and yield	CP or CPFEM databases	(He et al., 2024, Fuhg et al., 2022)
Calibration and UQ	CPFE, spectral CP, EBSD statistics, synthetic local/global data	(Dorward et al., 2023, Kumar et al., 24 May 2025, Pribe et al., 9 Mar 2026)
Constitutive discovery	DDD, PFC, DFT	(Akhondzadeh et al., 2020, Julian et al., 5 Sep 2025, Tsekenis et al., 2015, Shimanek et al., 2020)

The data modalities are equally heterogeneous. Some studies are almost entirely simulation-driven, with CP, Taylor, EVPFFT, or DDD providing labels (Frankel et al., 2019, Akhondzadeh et al., 2020). Others use experiments as direct inputs or validation targets: semi in situ EBSD during rolling (Saidi et al., 2021), HEDM-based microstructures for testing transferability (Pandey et al., 2020), EBSD-derived weld texture statistics for surrogate-based UQ (Kumar et al., 24 May 2025), DIC and EBSD fusion for stress reconstruction and fracture metrics (Koko et al., 4 Oct 2025), and DIC plus EBSD plus thermo-mechanical testing for Zircaloy-4 rate sensitivity identification (Liu et al., 2021). This distribution of data sources makes clear that “data-driven” in crystal plasticity is broader than neural-network emulation alone.

2. State representation, orientation space, and microstructural descriptors

A recurring theme is that data preparation is often as important as model architecture. The clearest case is orientation evolution in Euler space. In FCC aluminum rolling, crystal orientation is represented by Bunge Euler angles $(\phi_1,\Phi,\phi_2)$, with the same physical orientation appearing at multiple locations because of periodicity and cubic symmetry. The paper on preconditioned orientation learning shows that raw OEPs become artificially discontinuous near $\phi_1=\pi$ and $\phi_2=0,2\pi$, and that simply transferring trajectories into the fundamental zone does not remove the trainability problem (Saidi et al., 2021). The remedy is the modified orientation evolution path (MOEP): all 24 symmetry-equivalent trajectories are generated via

$g_i^j = O_i g^j,$

clustered by DBSCAN, and the continuous candidate containing the largest number of points inside the fundamental zone is selected. In that setting, preconditioning raises the ANN test score from $0.831$ to $0.999$, reduces training iterations by about an order of magnitude, and yields a preconditioned ANN whose disorientation distribution peaks at $30\%$0, with $30\%$1 of predictions below $30\%$2 (Saidi et al., 2021).

The same representational issue appears in other forms. In the 3D LSTM surrogate for copper, each voxel carries three Euler angles, and each training input is a $30\%$3 neighborhood, i.e.

$30\%$4

components, with the target equal to the center-voxel orientation at the next strain level (Pandey et al., 2020). That paper evaluates errors with a cubic-symmetry-aware disorientation metric, but does not symmetry-reduce the input representation itself. The practical implication is that physical symmetry can enter either before learning, during learning, or only in evaluation.

Microstructure descriptors also vary widely. Some surrogates use full spatial fields, such as $30\%$5 orientation images in oligocrystals (Frankel et al., 2019) or $30\%$6 orientation arrays in SC-DeepONet (He et al., 2024). Others deliberately reduce the microstructure to lower-dimensional summaries, such as the eight EBSD-derived texture component fractions $30\%$7 for 316L weldments (Kumar et al., 24 May 2025), or the single scalar texture spread $30\%$8 for a one-component cube texture family in convex yield learning (Fuhg et al., 2022). In the microstructure-sensitive GRU surrogate, grain seed positions and orientations are pooled to remove grain-swapping symmetry, so the encoder is permutation invariant at grain level (Atkinson et al., 8 Oct 2025).

Discretization is itself a representational choice. A large CPFE study comparing static mesh and grain-based mesh shows that both give reliable macroscopic stress–strain curves and localization locations, but static mesh smooths stress and strain profiles at grain boundaries, whereas grain-based mesh preserves discontinuities. Global stress deviations remain within $30\%$9, while local deviations reach up to $32\times 32$0 (Chen et al., 2023). For data-driven local-field modelling, the training labels are therefore discretization dependent.

3. Surrogate architectures and learned operators

The surrogate literature is structurally diverse because different targets demand different inductive biases. Sequence learning is dominant when the output is path dependent. In rolling texture evolution, a feed-forward ANN learns

$32\times 32$1

whereas a GRU predicts the next orientation from a short orientation history; after the same preconditioning, the GRU achieves a disorientation mode of $32\times 32$2 (Saidi et al., 2021). In voxelwise 3D orientation evolution under uniaxial tension, an LSTM surrogate trained on synthetic Dream.3D plus EVPFFT data reaches $32\times 32$3 of voxels within $32\times 32$4 for a $32\times 32$5 microstructure in a $32\times 32$6 step, and provides more than $32\times 32$7 speedup for $32\times 32$8 evolution relative to conventional EVPFFT on a large HEDM microstructure (Pandey et al., 2020).

When the target is a field rather than a sequence of scalar summaries, convolutional recurrence becomes advantageous. The hybrid Conv2D + ConvLSTM + Conv3D model for oligocrystal stress-field evolution predicts the full spatial field of the tensile-direction normal stress component from the initial orientation image and time sequence, preserving local stress concentrations and stress distributions through the elastic-plastic transition (Frankel et al., 2019). The paper is explicit, however, that this generalization is interpolation within a fixed data manifold: monotonic uniaxial tension at one strain rate, in $32\times 32$9 2D slices, with one stress component predicted.

Operator-learning approaches make the dependence on material and loading more explicit. The Material-Response-Informed DeepONet uses a ResUNet trunk for the microstructure and a branch network driven not by raw constitutive constants, but by 36 single-crystal stress–strain curves under the same loading and boundary conditions. The branch–trunk contraction is

$^2$0

Across four cases, including transfer to copper, shear, and cyclic loading, the model achieves $^2$1 above $^2$2, over $^2$3 of predicted stresses within $^2$4 relative error, and prediction speed almost $^2$5 times faster than CP simulations; with as few as 20 new data points and under 1 minute of fine-tuning, transfer learning remains accurate (He et al., 2024).

A related, but distinct, line learns macroscopic yield surfaces rather than full response trajectories. The pICNN-based yield model learns a signed-distance field $^2$6 from CPFEM yield databases while guaranteeing convexity with respect to stress by construction (Fuhg et al., 2022). This is not a field surrogate, but a reduced constitutive surrogate for initial yield.

Taken together, these studies suggest that surrogate design is target specific. Orientation updates favor sequence models; local stress fields favor spatiotemporal convolutional recurrence; homogenized response favors operator learning; and admissible macroscopic yield surfaces benefit from convexity-preserving architectures.

4. Constitutive discovery from lower-scale data

Not all data-driven crystal plasticity proceeds by emulating an existing CP solver. Several papers instead use lower-scale data to infer the constitutive law itself. A prominent example is the dislocation-density-based model extracted from more than 200 DDD simulations of single-crystal Cu under uniaxial tension (Akhondzadeh et al., 2020). There, the constitutive model has two parts: a generalized Taylor relation and a generalized Kocks–Mecking multiplication law. The DDD data support a logarithmic flow-stress dependence on slip-system strain rate, leading to

$^2$7

or equivalently an exponential slip-rate law that already subsumes Orowan (Akhondzadeh et al., 2020). The same DDD database shows that dislocation density can increase on systems with negligible $^2$8, which motivates a coplanar correction to Kocks–Mecking multiplication. The final model reproduces orientation-dependent hardening across the stereographic triangle and qualitatively matches experiments.

A more explicitly probabilistic variant appears in the active-learning GP flow-rule paper. There, the learned constitutive object is

$^2$9

with uncertainty-guided DDD acquisition in a dimension-mismatched Bayesian-optimization loop (Julian et al., 5 Sep 2025). The final model is validated against an independent test set of $(\phi_1,\Phi,\phi_2)$0 data points, the active learner converges in distribution within about 160 BO-guided simulations, and $(\phi_1,\Phi,\phi_2)$1 of test measurements fall within $(\phi_1,\Phi,\phi_2)$2 likelihood standard deviation of the predictive mean, close to the $(\phi_1,\Phi,\phi_2)$3 Gaussian benchmark (Julian et al., 5 Sep 2025). This is not a traditional fitted closed-form flow rule; it is a constitutive surrogate with explicit epistemic and aleatoric uncertainty.

Lower-scale data also motivate stochastic constitutive thinking. Phase field crystal simulations at finite temperature show avalanche statistics with

$(\phi_1,\Phi,\phi_2)$4

consistent with mean-field elastic depinning (Tsekenis et al., 2015). By contrast, 3D DDD under quasistatic stress control yields power-law avalanches whose average size grows roughly exponentially with applied stress and whose slip increases with system size at any applied stress, supporting an extended critical-like, glassy interpretation rather than a single tuned critical point (Lehtinen et al., 2016). A plausible implication is that constitutive surrogates for micron-scale plasticity may need stochastic, event-based outputs rather than smooth Gaussian fluctuations.

At the other end of the scale hierarchy, DFT-informed single-crystal Ni CPFEM replaces much of the usual experimental fitting by first-principles estimates of elastic constants, ideal shear strength, Peierls–Nabarro flow resistance, initial CRSS, and small-strain hardening slope (Shimanek et al., 2020). This is not machine learning, but it is data-informed crystal plasticity in the strong sense that lower-scale computational data are transferred into continuum constitutive parameters.

5. Calibration, uncertainty quantification, and experiment–model fusion

A major branch of data-driven crystal plasticity is devoted to inverse identification and uncertainty quantification. In one workflow, a Gaussian-process surrogate is trained on 160 or 320 CPFEM runs over an 8-dimensional parameter space, then used for Sobol analysis of yield stress, a post-yield stress increment, and tensile-curve NMSE in 316L stainless steel (Dorward et al., 2023). The surrogate reduces the cost of the sensitivity analysis from what would have required $(\phi_1,\Phi,\phi_2)$5 FE evaluations to only 320 FE simulations, and the subsequent reduced-parameter calibration shows that differential evolution is more reliable than Nelder–Mead because of local minima in the objective function (Dorward et al., 2023).

A second UQ strategy uses polynomial chaos expansion. For welded 316L stainless steel, eight EBSD-derived texture component fractions are sampled within physically observed bounds, CPFE is run on a statistically converged 120 $(\phi_1,\Phi,\phi_2)$6m RVE with about 615 grains, and a non-intrusive PCE surrogate is trained from only 200 CPFE simulations (Kumar et al., 24 May 2025). The surrogate reproduces held-out stress–strain curves graphically, provides mean and uncertainty bands, and identifies Cube and Goss as the dominant texture components for stress variability. Yield stress, stress at $(\phi_1,\Phi,\phi_2)$7, and stress at $(\phi_1,\Phi,\phi_2)$8 strain are all reported with mean, minimum, and maximum values from the surrogate (Kumar et al., 24 May 2025). The paper also illustrates a recurring limitation of the literature: graphical validation without explicit $(\phi_1,\Phi,\phi_2)$9, RMSE, or leave-one-out error.

The non-uniqueness of calibration from global data alone is addressed directly by a two-stage Bayesian workflow for synthetic Inconel 718. In stage 1, a neural-network surrogate is calibrated to 13 global stress points. In stage 2, a kernel-density estimate of the stage-1 posterior becomes the prior for a full spectral CP model calibrated jointly to global stress–strain data and 416 grain-average stresses, with posterior sampling performed by parallel sequential Monte Carlo (Pribe et al., 9 Mar 2026). The posterior is

$\phi_1=\pi$0

The main outcome is that local data sharply reduce uncertainty in $\phi_1=\pi$1 and $\phi_1=\pi$2, while the hardening pair $\phi_1=\pi$3 and $\phi_1=\pi$4 remains strongly correlated (Pribe et al., 9 Mar 2026).

Experimental data can also drive the constitutive model more directly. In Zircaloy-4, EBSD-informed microstructure reconstruction and DIC strain histories near a notch are used to identify the thermally activated slip parameters $\phi_1=\pi$5 and $\phi_1=\pi$6, while elevated-temperature tensile data determine a temperature-dependent prismatic CRSS law (Liu et al., 2021). In a different direction, the crack-growth study in AA-5052 does not predict deformation forward from loading; instead it imposes measured DIC displacements directly as nodal boundary conditions on an EBSD-informed anisotropic elastic or crystal-plastic model to reconstruct stress, local $\phi_1=\pi$7, $\phi_1=\pi$8, and $\phi_1=\pi$9 (Koko et al., 4 Oct 2025). This demonstrates a data-driven crystal plasticity mode in which CP acts as a mechanically consistent stress-reconstruction engine.

6. Scope, limitations, and open directions

Several misconceptions are corrected by this body of work. First, data-driven crystal plasticity does not generally replace constitutive theory with an unconstrained black box. Many surrogates emulate a chosen physics engine: the fully constrained Taylor model in rolling texture evolution (Saidi et al., 2021), CPFE for oligocrystal stress fields (Frankel et al., 2019), EVPFFT for voxelwise orientation evolution (Pandey et al., 2020), or CP-generated mean-field response in DeepONet (He et al., 2024). In such cases, the surrogate cannot be more accurate than the model that generated its labels unless the data source itself is improved.

Second, poor performance is often blamed on architecture when the dominant issue is geometry or representation. The rolling-texture paper argues that discontinuous Euler-space trajectories, not ANN architecture per se, are the main obstacle to learning (Saidi et al., 2021). The discretization study likewise shows that local-field labels differ systematically depending on whether the microstructure is represented at the integration-point or element level (Chen et al., 2023).

Third, generalization remains narrow in much of the current literature. The ConvLSTM stress-field model is validated on unseen microstructures from the same DREAM.3D slicing process and the same monotonic tension protocol, not on new loading families or material systems (Frankel et al., 2019). The 3D LSTM orientation surrogate is limited to FCC Cu, uniaxial tension, fixed strain-step size, and local $\phi_2=0,2\pi$0 neighborhoods, with long-range interactions neglected (Pandey et al., 2020). The PCE and GP-based calibration papers are likewise specialized to moderate-dimensional parameter or texture spaces and smooth output statistics (Kumar et al., 24 May 2025, Dorward et al., 2023). The microstructure-sensitive GRU paper explicitly notes that out-of-distribution microstructures are harder to predict, particularly heavily textured ones (Atkinson et al., 8 Oct 2025).

Fourth, constitutive identifiability is a persistent issue. Global curves alone often leave large degeneracies in hardening parameters (Pribe et al., 9 Mar 2026). Even when local data are added, correlated parameters can remain only partially identifiable. This suggests that future progress will depend as much on experimental design and observable choice as on regression architecture.

The literature also points toward several extensions. One obvious direction is to combine the orientation-preconditioning idea with richer CP data sources such as VPSC, CPFEM, or experimental 4D orientation histories (Saidi et al., 2021). Another is to retain the strong physical backbone of finite-strain formulations based on additive elastic corrector rates, while learning only slip kinetics, hardening, or hyperelastic closures (Zhang et al., 2020). Active learning from DDD offers a path to semi-autonomous multiscale calibration (Julian et al., 5 Sep 2025), whereas Bayesian two-stage workflows indicate how local diffraction-like data can make full-field CP calibration tractable (Pribe et al., 9 Mar 2026). More broadly, this literature suggests that the most durable form of data-driven crystal plasticity is likely to remain hybrid: representation-aware, symmetry-consistent, physically constrained, and explicit about the fidelity limits inherited from its data source.