[Paper Review] Two-stage 2D-to-3D reconstruction of realistic microstructures: Implementation and numerical validation by effective properties

Paul Seibert, Alexander Raßloff+5 more|arXiv (Cornell University)|Jan 23, 2023

Machine Learning in Materials ScienceMaterials Science3 citations

TL;DR

This paper presents a two-stage, differentiable 2D-to-3D microstructure reconstruction method that enhances the DMCR algorithm by refining reconstructions using statistical descriptors. Validated on real CT scans of a β-Ti/TiFe alloy and synthetic spinodoid structures, the method achieves high accuracy in predicting effective elastic and plastic properties, with errors reduced to below 1% when using representative 2D slices and descriptor averaging.

ABSTRACT

Realistic microscale domains are an essential step towards making modern multiscale simulations more applicable to computational materials engineering. For this purpose, 3D computed tomography scans can be very expensive or technically impossible for certain materials, whereas 2D information can be easier obtained. Based on a single or three orthogonal 2D slices, the recently proposed differentiable microstructure characterization and reconstruction (DMCR) algorithm is able to reconstruct multiple plausible 3D realizations of the microstructure based on statistical descriptors, i.e., without the need for a training data set. Building upon DMCR, this work introduces a highly accurate two-stage reconstruction algorithm that refines the DMCR results under consideration of microstructure descriptors. Furthermore, the 2D-to-3D reconstruction is validated using a real computed tomography (CT) scan of a recently developed beta-Ti/TiFe alloy as well as anisotropic "bone-like" spinodoid structures. After a detailed discussion of systematic errors in the descriptor space, the reconstructed microstructures are compared to the reference in terms of the numerically obtained effective elastic and plastic properties. Together with the free accessibility of the presented algorithms in MCRpy, the excellent results in this study motivate interdisciplinary cooperation in applying numerical multiscale simulations for computational materials engineering.

Motivation & Objective

• To address the challenge of generating realistic 3D microstructures from limited 2D microscopy data when 3D CT scans are unavailable or impractical.
• To improve upon existing data-free, differentiable reconstruction methods by introducing a two-stage refinement process based on statistical descriptors.
• To validate the reconstructed microstructures using both real CT data and synthetic anisotropic structures, focusing on predictive accuracy of effective mechanical properties.
• To quantify systematic errors in descriptor space and assess the impact of slice size and smoothing on reconstructed microstructure fidelity.
• To enable reliable multiscale simulations in computational materials engineering by providing a free, open-source implementation via MCRpy.

Proposed method

• Adapt the differentiable microstructure characterization and reconstruction (DMCR) algorithm to generate initial 3D microstructure realizations from single or orthogonal 2D slices.
• Implement a two-stage optimization: first generate a 3D reconstruction via DMCR, then refine it using gradient-based optimization that minimizes the discrepancy between target and reconstructed statistical descriptors.
• Use a set of statistical descriptors—such as two-point correlation functions and lineal path functions—as the basis for the differentiable loss function in the refinement stage.
• Apply descriptor-based smoothing to correct noise-induced artifacts, ensuring that microstructural features like sharp corners are preserved without over-smoothing.
• Perform numerical homogenization to compute effective elastic and plastic properties of reconstructed microstructures and compare them to reference values from real CT scans.
• Use descriptor averaging across multiple small 2D slices to improve representativeness when the original slice is too small, mitigating sampling bias.

Experimental results

Research questions

• RQ1 Can a two-stage differentiable reconstruction method significantly improve the accuracy of 3D microstructures reconstructed from 2D slices compared to baseline DMCR?
• RQ2 How do errors in statistical descriptors propagate into errors in predicted effective mechanical properties (elastic and plastic)?
• RQ3 To what extent does the size of the 2D slice used for descriptor computation affect the fidelity of the reconstructed 3D microstructure?
• RQ4 How does descriptor-based smoothing compare to standard Gaussian smoothing in preserving microstructural features and improving effective property predictions?
• RQ5 Can averaging descriptors from multiple small 2D slices effectively compensate for the lack of a large representative slice?

Key findings

• The two-stage reconstruction method reduces errors in effective Young’s modulus to within -0.5% for columnar and -8.4% for lamellar spinodoid structures when descriptors are averaged over multiple small slices, compared to -7.8% and -11% for a single small slice.
• Using a large single slice for descriptor computation results in errors of only -2.1% (columnar) and -2.0% (lamellar) in effective Young’s modulus, demonstrating the importance of representative sampling.
• Descriptor-based smoothing recovers original microstructural features such as sharp corners, while Gaussian smoothing fails to distinguish noise from real features, leading to significant errors.
• Smoothing increases effective yield strength by up to 0.5% in the columnar structure and 0.3% in the lamellar structure, indicating that noise correction enhances mechanical prediction accuracy.
• Unsmoothed reconstructions show lower stiffness (e.g., -1.3% for columnar, -4.1% for lamellar) due to spurious assignment of softer phases in stiff regions, which weakens the effective response.
• The method achieves high predictive accuracy for anisotropic effective behavior, with reconstructed properties closely matching those of real CT scans, validating its use in multiscale simulations.