[Paper Review] Reconstructing microstructures from statistical descriptors using neural cellular automata

Paul Seibert, Alexander Raßloff+5 more|arXiv (Cornell University)|Sep 28, 2023

Cellular Automata and Applications4 citations

TL;DR

This paper proposes a neural cellular automaton (NCA)-based method for reconstructing complex microstructures from statistical descriptors, bypassing the need for large image datasets. By training on descriptors rather than images, the NCA learns to evolve microstructures using only local rules, enabling scalable, parallelizable, and highly efficient generation of large-scale 2D microstructures with long-range correlations, outperforming traditional descriptor-based methods in speed and scalability.

ABSTRACT

The problem of generating microstructures of complex materials in silico has been approached from various directions including simulation, Markov, deep learning and descriptor-based approaches. This work presents a hybrid method that is inspired by all four categories and has interesting scalability properties. A neural cellular automaton is trained to evolve microstructures based on local information. Unlike most machine learning-based approaches, it does not directly require a data set of reference micrographs, but is trained from statistical microstructure descriptors that can stem from a single reference. This means that the training cost scales only with the complexity of the structure and associated descriptors. Since the size of the reconstructed structures can be set during inference, even extremely large structures can be efficiently generated. Similarly, the method is very efficient if many structures are to be reconstructed from the same descriptor for statistical evaluations. The method is formulated and discussed in detail by means of various numerical experiments, demonstrating its utility and scalability.

Motivation & Objective

• To develop a scalable and efficient method for microstructure reconstruction that avoids reliance on large image datasets.
• To integrate principles from simulation, Markov random fields, deep learning, and descriptor-based approaches into a unified framework.
• To enable high-resolution and large-scale microstructure generation by leveraging local update rules in a neural cellular automaton.
• To achieve fast sampling of microstructures from trained models, especially for statistical evaluations involving many realizations.
• To explore the feasibility of extending the method to 3D microstructure reconstruction from 2D or 3D reference data.

Proposed method

• A neural cellular automaton (NCA) is trained to evolve microstructures based on local neighborhood information and statistical descriptors, not image data.
• The NCA uses a small neural network to learn a partial differential equation-like update rule for each pixel based on its local context.
• Hidden dimensions in the microstructure representation enable long-range correlations despite purely local updates.
• Training is performed using statistical descriptors (e.g., two-point correlation functions) derived from a single reference microstructure.
• Sampling during inference is fully parallelizable, as each pixel update depends only on its local neighborhood and the NCA’s learned dynamics.
• The method decouples expensive descriptor evaluation and optimization into the training phase, enabling fast inference for large-scale reconstructions.

Experimental results

Research questions

• RQ1 Can a neural cellular automaton reconstruct complex microstructures using only statistical descriptors, without requiring a dataset of reference micrographs?
• RQ2 How does the NCA-based method scale in terms of computational cost when generating large or numerous microstructure realizations?
• RQ3 To what extent can local update rules in an NCA capture long-range morphological correlations in heterogeneous materials?
• RQ4 How does the NCA-based approach compare in efficiency and accuracy to established descriptor-based reconstruction methods like DMCR?
• RQ5 Can the method be extended to 3D microstructure reconstruction from 2D or 3D reference data?

Key findings

• The NCA-based method achieves linear scaling in computational cost with respect to the number of pixels during inference, enabling efficient generation of large microstructures such as 4096²-pixel reconstructions.
• Sampling from a trained NCA is significantly faster than traditional descriptor-based methods like DMCR, especially for large-scale or repeated reconstructions.
• The method demonstrates superior scalability: training cost is independent of reconstruction size, and sampling scales sub-linearly in growth rate compared to DMCR.
• The NCA successfully captures long-range correlations in microstructures despite relying only on local update rules, thanks to hidden state dimensions in the microstructure representation.
• The approach is inherently parallelizable due to its local, self-assembling nature, enabling efficient distribution across computational resources.
• The method outperforms DMCR in sampling speed and scalability, with the training cost being amortized over many reconstructions, making it ideal for statistical evaluations.