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Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials
Sehyun Chun, Sidhartha Roy, Yen Thi Nguyen, Joseph B. Choi, H. S. Udaykumar, Stephen S. Baek
TL;DR
Because heterogeneous energetic-material sensitivity depends on stochastic microstructure, statistically representative ensembles are needed for meso-scale simulations, though suitable imaged data are limited. This paper uses a GAN to generate synthetic microstructures and reports that they replicate real structures while enabling controlled, spatially varied morphology.
Problem
Statistically meaningful meso-scale simulations require ensembles of representative microstructures, but image data are costly to acquire and limited across materials and formulations.
Source: §1.1 · p. 2Method
A GAN generates synthetic microstructures using local stochasticity and global morphology parameters, with morphology control available across spatial regions.
Source: §1.3 · p. 4, §2.3 · p. 11Results
The method produces microstructures that qualitatively and quantitatively replicate real images and can vary morphology spatially and seamlessly.
Source: §3 · p. 11Takeaways & Limitations
Spatial control of morphology supports exploring and designing microstructures within a materials-by-design framework.
Source: §2.3 · p. 11, §3 · p. 12The single-scale morphology parameter cannot capture large crystal-size variation, and the GAN could not generate crystals larger than 125 pixels.
Source: §3 · p. 11
Abstract
from arXiv · showhide
The sensitivity of heterogeneous energetic (HE) materials (propellants, explosives, and pyrotechnics) is critically dependent on their microstructure. Initiation of chemical reactions occurs at hot spots due to energy localization at sites of porosities and other defects. Emerging multi-scale predictive models of HE response to loads account for the physics at the meso-scale, i.e. at the scale of statistically representative clusters of particles and other features in the microstructure. Meso-scale physics is infused in machine-learned closure models informed by resolved meso-scale simulations. Since microstructures are stochastic, ensembles of meso-scale simulations are required to quantify hot spot ignition and growth and to develop models for microstructure-dependent energy deposition rates. We propose utilizing generative adversarial networks (GAN) to spawn ensembles of synthetic heterogeneous energetic material microstructures. The method generates qualitatively and quantitatively realistic microstructures by learning from images of HE microstructures. We show that the proposed GAN method also permits the generation of new morphologies, where the porosity distribution can be controlled and spatially manipulated. Such control paves the way for the design of novel microstructures to engineer HE materials for targeted performance in a materials-by-design framework.
1 Introduction
Energetic-material sensitivity is tied to stochastic microstructure and hot-spot formation, motivating predictive models informed by ensembles of meso-scale simulations. This section motivates synthetic microstructures and introduces a GAN designed to reproduce and control their morphology.
1 Introduction
- HE sensitivity depends on stochastic micro-morphology, where energy localization creates hot spots that initiate reactions and can culminate in detonation.The introduction frames microstructural control as relevant to safety and performance design.Source: §1 · pp. 1–2
1.1 Need for ensemble simulations on synthetic microstructures
- Ensembles of representative microstructures are needed for statistically meaningful meso-scale simulations, but imaged data are costly and often limited in material and formulation scope.Synthetic microstructures can serve as proxies for real samples in in-silico experiments.Source: §1.1 · p. 2
1.2 Previous approaches
- Packing and tessellation methods can miss realistic, non-ideal features and local structure, limiting representation of morphologies relevant to sensitivity.The cited examples include cracks, tortuous voids, inter-void distances, void shapes, and orientations.Source: §1.2 · pp. 2–3
1.3 A method for microstructure generation using GAN
- The proposed patch-based, fully convolutional GAN uses local stochasticity ρ and global morphology λ to generate realistic microstructures with controllable morphology and arbitrary image dimensions.The architecture provides patch-wise feedback and can vary λ to control morphology; varying input-tensor size produces arbitrary-sized images without stitching.Source: §1.3 · pp. 3–4, Figure 1 · p. 4
2 Results
GAN-generated microstructures generally resemble real samples and reproduce their simulated shock response. The GAN also provides controls for varying morphology, enabling stochastic ensembles, continuous transitions, and spatially patterned microstructures.
2.1 Qualitative and quantitative comparison of real and synthetic microstructures
- GAN-SynµS visually resemble RealµS without the artifacts and blurry crystal boundaries observed in transfer-learning samples, while both methods generally match void morphometry.The comparison covers void diameter, aspect ratio, and orientation distributions; generated void-size and aspect-ratio peaks shift slightly, while orientation distributions agree well.Source: §2.1 · p. 5, Figure 2 · p. 5
2.2 Simulations of reactive dynamics in real and synthetic microstructures
- GAN-SynµS reproduce RealµS temperature and pressure fields and hot-spot-area evolution under shock loading, supporting their use as proxies in ensemble simulations of pressed HMX.The simulated RealµS and SynµS are 25µm × 25µm and are shock-loaded at 9.5 GPa.Source: §2.2 · pp. 6–7, Figure 5 · p. 7, Figure 6 · p. 7
2.3 Towards materials-by-design: Controlling the micro-morphology
- Varying global morphology parameter λ changes crystal and void size distributions or orientations, while varying local stochasticity parameter ρ changes local layouts and details at similar overall morphology.Examples show λ widening crystal-size distributions and making void sizes bimodal, or shifting void orientations; ρ produces stochastic variations for fixed λ.Source: §2.3 · p. 8, Figure 7 · p. 8, Figure 8 · p. 9
- Linear interpolation of λ produces smoothly varying microstructures, including nearly linear grain-size growth, whereas the attempted transfer-learning interpolation does not vary smoothly.The GAN’s λ parameter maps morphology continuously between two endpoint microstructures.Source: §2.3 · p. 9, Figure 9 · p. 10
- Small-crystal/void SynµS develop more hot spots and higher pressure than large-crystal/void SynµS, with a larger hot-spot growth rate.The compared mean crystal sizes are approximately 1µm and 2.5µm, respectively.Source: §2.3 · p. 9, Figure 10 · p. 10, Figure 11 · p. 11
- Spatially varying λ creates graded or patterned crystal and void sizes without observable stitching boundaries, and could allow more precise control of energetic-material burning rate.The demonstrated graded sample transitions from smaller features at one end to larger features at the other.Source: §2.3 · p. 11
3 Discussion
The GAN generates realistic synthetic microstructures with continuous, spatially controlled morphology, supporting morphology-engineered materials-by-design. Its current single-scale parameterization limits the crystal-size range, while ensemble simulations are proposed for future sensitivity studies.
3 Discussion
- The GAN generates microstructures that qualitatively and quantitatively replicate real samples, with arbitrary-size generation, continuous morphology control, and spatially controlled morphology.The method avoids stitching or quilting.Source: §3 · p. 11
- The current single-scale morphology parameter cannot capture broad crystal-size variation, and the generator did not produce crystals larger than 125 pixels.The authors are exploring multi-scale GAN architectures to address this range limitation.Source: §3 · p. 11
- The authors propose ensemble simulations on morphology-controlled microstructures to characterize how morphology affects hot-spot ignition and growth and to develop surrogate models linking meso-scale behavior to macro-scale simulations.They describe this as a route toward engineering HE morphology for desired performance.Source: §3 · pp. 11–12
- A spatially graded λ interpolates linearly between small-crystal and large-crystal morphology parameters; painting λ regions creates a corresponding patterned microstructure.The figure demonstrates a Hawkeye pattern imprinted into the crystal-size distribution without observable stitching boundaries or awkward transitions.Source: Figure 12 · p. 12, §3 · p. 12
4 Methods
The methods train a GAN on cropped SEM images of pressed HMX and provide a way to control generated morphology across a spatial grid. Morphometry and reactive meso-scale simulations quantify microstructural features and shock response, including hot-spot evolution.
4.1 Data
- 12,500 randomly cropped 161 × 161 patches from a 3,000 × 3,000 SEM image of pressed HMX formed the GAN training set.At 52 nm per pixel, each patch represents 8.5 µm × 8.5 µm.Source: §4.1 · p. 12
4.2 GAN
- The GAN trains a generator against a discriminator, using an averaged loss evaluated across grid patches.At inference, users can vary the global morphology parameter across grid locations; each parameter controls a 125 × 125 receptive-field window.Source: §4.2 · p. 13
4.3 Morphometry
- Morphometry quantifies void and crystal size, shape, and orientation distributions, and uses two-point correlation functions to characterize phase structure.The two-point function measures the probability that two points separated by a chord vector lie in the same phase; here the indicator identifies voids.Source: §4.3 · p. 13
4.4 Meso-scale simulations of reactive mechanics
- Reactive meso-scale simulations track hot-spot area over time, defining it as the domain area where temperature exceeds the planar-shock temperature Tbulk.The simulations model shock-driven void collapse; hotter hot spots are associated with higher chemical decomposition rates.Source: §4.4 · pp. 13–14