Microstructural Materials Design via Deep Adversarial Learning Methodology

Zijiang Yang; Xiaolin Li; L. Catherine Brinson; Alok N. Choudhary; Wei Chen; Ankit Agrawal

Source-linked AI summary

Microstructural Materials Design via Deep Adversarial Learning Methodology

Zijiang Yang, Xiaolin Li, L. Catherine Brinson, Alok N. Choudhary, Wei Chen, Ankit Agrawal

arXiv:1805.02791v2May 8, 2018cond-mat.mtrl-sciphysics.comp-ph

TL;DR

Existing microstructure characterization and reconstruction methods may lack usable design variables or lose important information through dimension reduction. The paper trains GANs to map low-dimensional latent variables to microstructures, uses those variables with Bayesian optimization for property-driven design, and demonstrates scalability and transfer learning, with reported performance values of 0.6827 and 0.7630 in the case study.

Problem
Existing MCR approaches may lack parameters suitable as design variables or lose important microstructural information through dimension reduction.
Method
GANs learn mappings from prespecified-dimensional latent variables to microstructures, after which Bayesian optimization searches latent design variables using property evaluations.
Results
0.6827 was the reported GAN-generator performance, 4.8% greater than the 0.6509 baseline, while another reported performance was 0.7630 versus randomly sampled microstructures.
Takeaways & Limitations
The methodology provides prespecified-dimensional latent design variables, scalable generation of arbitrary-sized microstructures, and discriminator reuse for structure-property prediction.
Takeaways & Limitations
Processing or manufacturing constraints are not considered in the design optimization.

Abstract

from arXiv · show

Identifying the key microstructure representations is crucial for Computational Materials Design (CMD). However, existing microstructure characterization and reconstruction (MCR) techniques have limitations to be applied for materials design. Model-based MCR approaches do not have parameters that can serve as design variables, while MCR techniques that rely on dimension reduction tend to lose important microstructural information. In this work, we present a deep adversarial learning methodology that overcomes the limitations of existing MCR techniques. In the proposed methodology, generative adversarial networks (GAN) are trained to learn the mapping between latent variables and microstructures. Thereafter, the low-dimensional latent variables serve as design variables, and a Bayesian optimization framework is applied to obtain microstructures with desired material property. Due to the special design of the network architecture, the proposed methodology is able to identify the latent (design) variables with desired dimensionality, as well as minimize the information loss even for complex material microstructures. The validity of the proposed methodology is tested numerically on a synthetic microstructure dataset and its effectiveness for materials design is evaluated through a case study of optimizing optical performance for energy absorption. In addition, the scalability and transferability of proposed methodology are also demonstrated in this work. Specifically, the proposed methodology is scalable to generate arbitrary sized microstructures, and it can serve as a pre-trained model to improve the performance of a structure-property predictive model via transfer learning.

1. INTRODUCTION

Microstructure representation is central to computational materials design, but selecting useful design variables from existing characterization and reconstruction methods remains challenging.

Microstructure representation determines the success of microstructural materials design.
Existing practice selects microstructural design variables from characteristics obtained through microstructure characterization and reconstruction techniques.
The introduction organizes existing microstructure characterization and reconstruction techniques into categories.

5. Deep Belief Network-based methods [22]

The section identifies Spectral Density Function-based methods as one category of existing microstructure characterization and reconstruction techniques.

Spectral Density Function-based methods are listed among existing microstructure characterization and reconstruction approaches.

7. Transfer Learning-based methods [23, 24]

The paper frames existing microstructure representations and generative approaches as limited for materials design, then presents a scalable GAN methodology with low-dimensional latent design variables, Bayesian optimization, and transfer learning.

Some existing MCR methods are not applicable to microstructural materials design, while applicable methods can lose dispersive or geometrical information.
Dimension reduction can remove structural information and does not guarantee that new microstructures can be generated by sampling reduced dimensions.
Generative models learn low-dimensional latent variables that can serve as design variables for generating high-dimensional microstructures.
The paper positions GANs as an unexplored application in computational materials design despite prior use for reconstructing different microstructure types.
The proposed workflow uses a scalable GAN to learn prespecified-dimensional latent variables, propagates them through the generator, evaluates material properties physically, and applies GP-Hedge Bayesian optimization.
The methodology provides a low-dimensional nonlinear embedding intended to preserve microstructural information without geometrical or dispersive approximations or removal of dimensions.
The approach is designed to generate arbitrary-sized microstructures and reuse discriminator weights to facilitate structure-property predictive models.

2. Microstructural Design Representation using Deep Adversarial Learning

The methodology uses GANs to map latent variables to microstructures, treating the latent code as design variables. Its architecture and composite losses are designed for dimensional flexibility, morphological fidelity, and training stability.

Generative adversarial learning: GAN training learns a generator mapping latent variables to microstructures and a discriminator distinguishing generated from real samples.
Generative adversarial learning: The latent variables become microstructure design variables once the generator produces realistic samples at adversarial equilibrium.
Network architecture: The proposed architecture uses symmetric convolutional generator and discriminator networks, replacing fully connected layers to support scalability.
Network architecture: The number of layers can be assigned flexibly, provided the generator and discriminator retain the required symmetry.
Loss function: The total loss combines adversarial, style-transfer, and model-collapse components to evaluate realism, impose morphology constraints, and prevent collapse.
Numerical validation: Generated microstructures visually resemble training samples, while mean correlation functions match and generated envelopes cover the original data range.

3. Microstructure Design Evaluation

Design evaluation propagates latent design variables through the GAN generator and then evaluates each generated microstructure with physics-based simulation. In the case study, Rigorous Coupled Wave Analysis supplies optical absorption performance.

Evaluation pipeline: The evaluation pipeline first converts latent design variables into microstructure images using the trained GAN generator.
Evaluation pipeline: Physics-based simulation then maps each generated microstructure to its material property or structural performance.
Optical case study: Rigorous Coupled Wave Analysis is used in the case study to simulate optical absorption performance.

4. Microstructure Design Synthesis

The methodology uses GAN-derived latent variables as low-dimensional microstructure design variables and searches them with simulation-based Bayesian optimization. Gaussian Process metamodeling and GP-Hedge adaptively reduce expensive evaluations while improving optical absorption.

Design formulation: GAN latent variables serve as bounded, independent microstructure design variables for simulation-based design synthesis.The variables are constrained to [-1, 1] and mapped to microstructures by generator G(z).
Bayesian optimization: A 250-point Latin Hypercube design in the 9-dimensional latent space initializes the response surface model for Bayesian optimization.Each sampled latent design is paired with its simulated optical performance.
Bayesian optimization: Gaussian Process metamodeling estimates performance and uncertainty at unexplored designs, allowing expensive evaluations to focus on promising candidates and reducing overall computational cost.GP-Hedge probabilistically selects among expected improvement, probability of improvement, and lower confidence bound criteria.
Optimization results: The optimized microstructure reaches optical performance 0.7630, exceeding randomly sampled microstructures’ mean 0.6509 by 17.2%.GAN-generated random samples have mean performance 0.6827, 4.8% above the randomly sampled training structures; the theoretical upper bound is 1.0.

5. Scalability and Transferability

The proposed model scales microstructure size by changing latent-variable dimensionality and transfers discriminator knowledge to structure-property prediction. These capabilities extend the methodology beyond a fixed design representation and can improve predictive-model development.

Scalability: The architecture permits prescribed latent-variable dimensionality while retaining negligible information loss for complex microstructural geometries.This is presented as a central advantage of the proposed deep adversarial learning model.
Scalability: Adding convolutional layers increases the image-to-latent scaling factor by 4, enabling a 96 × 96 image to map to 3 × 3 latent variables through five layers.The 96/3 = 32 scaling factor is achieved as 2^5.
Scalability: Lower latent dimensionality can reduce optimization cost but increases GAN training cost, creating a trade-off governed by available computational resources.Higher dimensionality can reduce GAN training burden when design optimization is not resource-limited.
Scalability: Changing latent-variable dimensionality controls generated-image size without retraining, and experiments demonstrate arbitrary-sized microstructures for the material system.Output-size variation can support analyses involving SVEs and RVEs.
Transferability: Transfer learning initializes a structure-property regressor with discriminator architecture and weights learned from the GAN microstructure dataset.The transferred model uses discriminator convolutional layers before appending fully connected regression layers.

6. Conclusion and Future Work

The proposed deep adversarial learning methodology integrates GAN-based microstructure generation with Bayesian optimization, using latent variables as design variables. It reduces information loss, supports flexible dimensionality, lowers evaluation cost, and offers scalability and transfer-learning reuse, while leaving several extensions for future work.

Methodology: The methodology trains a GAN on microstructures, then uses latent variables as design variables in Bayesian optimization for desired material properties.Gaussian Process metamodeling updates the design-variable/performance relationship, and GP-Hedge proposes the next sampling point.
Contributions: The end-to-end design loop reduces information loss and preserves more microstructural characteristics than the reconstruction approach is intended to retain.The methodology extends GANs into the materials-design loop rather than limiting them to reconstruction.
Contributions: GP-Hedge Bayesian optimization uses Gaussian Process metamodeling to reduce design evaluations, decreasing computational cost while improving design performance.The metamodel is incorporated into the optimization process to guide candidate selection.
Contributions: A customized loss function and network architecture support generation of new microstructures with similar characteristics and flexible latent-variable dimensionality.The network and training parameters may also be reused as starting points for other materials-science deep-learning applications.
Future Work: The methodology's broader applicability remains to be established for sharp-featured, crystalline, grain-boundary, multiphase, and continuous-phase microstructures.The authors identify these material classes as directions for extending the demonstrated impact.
Future Work: Processing and manufacturing constraints are not included in the design optimization; incorporating them requires establishing a processing-structure-property linkage.Future work also proposes relating latent variables to processing or manufacturing parameters and adding appropriate optimization constraints.
Future Work: Future studies should examine latent-variable dimensionality, its impact on network training, and methods for stabilizing training.Suggested modeling directions include Wasserstein GANs for model collapse, ResNet structures for learning capability, and visual attention for interpretation.