Neural Network Modeling of Microstructure Complexity Using Digital Libraries

TL;DR

The assessment suggests that the leaky integrate-and-fire neuron model offers superior predictive accuracy with fewer parameters and less memory usage, alleviating the accuracy-cost tradeoff in contrast to the common practices in computer vision tasks.

Abstract

Microstructure evolution in matter is often modeled numerically using field or level-set solvers, mirroring the dual representation of spatiotemporal complexity in terms of pixel or voxel data, and geometrical forms in vector graphics. Motivated by this analog, as well as the structural and event-driven nature of artificial and spiking neural networks, respectively, we evaluate their performance in learning and predicting fatigue crack growth and Turing pattern development. Predictions are made based on digital libraries constructed from computer simulations, which can be replaced by experimental data to lift the mathematical overconstraints of physics. Our assessment suggests that the leaky integrate-and-fire neuron model offers superior predictive accuracy with fewer parameters and less memory usage, alleviating the accuracy-cost tradeoff in contrast to the common practices in computer vision tasks. Examination of network architectures shows that these benefits arise from its reduced weight range and sparser connections. The study highlights the capability of event-driven models in tackling problems with evolutionary bulk-phase and interface behaviors using the digital library approach.

Figures (5)

• Figure 1: Representations of spatiotemporal complexity.(a) Turing patterns in nature. (b) Evolution of physical systems in pixel/voxel representations, encompassing information not necessary for the governing physical laws. (c) Interfaces play a crucial role in characterizing the development of physical systems. (d) Artificial neurons, which can be used to process continuously evolving pixel/voxel information. (e) Spiking neurons, capable of processing information driven by event-based spikes.
• Figure 2: Neural network prediction using artificial and spiking neurons.(a) Neural networks separately process spatial and temporal information and combine them subsequently within artificial neural networks (ANNs). (b) In spiking neural networks (SNNs), spatiotemporal data is processed in an integrated manner by neural networks. (c-f) The architectures of advanced spatiotemporal predictive models include ConvLSTM (c), PredRNN++ (d), and SimVP (e) based on ANNs, as well as STCLIF (f) based on SNNs. ${\rm f}_t$, ${\rm i}_t$, ${\rm g}_t$, and ${\rm o}_t$ are forget gate, input gate, input-modulation gate, and output gate, respectively. ${\bf X}$, ${\bf H}$, ${\bf C}$, ${\bf M}$, ${\bf S}$, ${\bf V}$ are inputs, hidden states, temporal cell states, spatiotemporal memory states, spiking input, and membrane potentials, respectively. Superscripts denote the layer index, while subscripts represent the time step. The symbols $\otimes$, $\oplus$, and $\parallel$ represent the Hadamard product, pointwise addition, and concatenation operation, respectively.
• Figure 3: Interface representations in microstructure evolution.(a) Sharp and diffuse interfaces in modeling microstructure evolution. (b) Fatigue crack growth (FCG) with sharp interfaces. (c) FCG prediction using base ANN (RNN and LSTM) and SNN models. (d) Evolution of Turing patterns with diffuse interfaces. (e) Limitations of base ANN/LSTM and SNN models in predicting Turing patterns. (f) Predicted microstructure evolution for Turing patterns using advanced spatiotemporal predictive models.
• Figure 4: Accuracy and cost of microstructure evolution prediction.(a) Mean absolute error (MAE) of FCG prediction and ground truth of the crack morphologies (Eq. 8). (b) The number of parameters used in the neural network model for FCG prediction. (c) MAE of Turing patterns prediction and ground truth of the microstructures (Eq. 8). (d) The accuracy-cost map of advanced spatiotemporal models (ConvLSTM, PredRNN++, SimVP, STCLIF) in predicting Turing patterns.
• Figure 5: Neural network architectures.(a) Weights distribution of convolutional layers in ConvLSTM and STCLIF models. (b) Connectivity patterns in ConvLSTM and STCLIF models.