An efficient optimization based microstructure reconstruction approach with multiple loss functions

Abstract

Stochastic microstructure reconstruction involves digital generation of microstructures that match key statistics and characteristics of a (set of) target microstructure(s). This process enables computational analyses on ensembles of microstructures without having to perform exhaustive and costly experimental characterizations. Statistical functions-based and deep learning-based methods are among the stochastic microstructure reconstruction approaches applicable to a wide range of material systems. In this paper, we integrate statistical descriptors as well as feature maps from a pre-trained deep neural network into an overall loss function for an optimization based reconstruction procedure. This helps us to achieve significant computational efficiency in reconstructing microstructures that retain the critically important physical properties of the target microstructure. A numerical example for the microstructure reconstruction of bi-phase random porous ceramic material demonstrates the efficiency of the proposed methodology. We further perform a detailed finite element analysis (FEA) of the reconstructed microstructures to calculate effective elastic modulus, effective thermal conductivity and effective hydraulic conductivity, in order to analyse the algorithm's capacity to capture the variability of these material properties with respect to those of the target microstructure. This method provides an economic, efficient and easy-to-use approach for reconstructing random multiphase materials in 2D which has potential to be extended to 3D structures.

Reinforcement Learning based Sequential Batch-sampling for Bayesian Optimal Experimental Design

“…Optimizing black-box functions and using GP regression as an agent has been done in [35] and [37,38] respectively. The task of constructing optimization algorithms with neural networks [39,40,41] that rival state of the art methods such as Adaptive Moment Estimation (Adam) using RL has been accomplished [35]. where the authors use the guided policy search RL method for searching in large sets of involved potential policies.…”

Stress field prediction in fiber-reinforced composite materials using a deep learning approach

“…Bock et al [8] presents a detailed overview of data mining and machine learning approaches to model process-microstructure-propertyperformance chain in the descriptive-predictive-prescriptive format. Applications include modeling effects of process parameters on microstructure, microstructure reconstruction [9,10], and capturing localized elastic strain in composites among several others. Pathan et al [11] has used a gradientboosted tree regression model to predict the homogenized properties such as macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane.…”

Descriptor-based reconstruction of three-dimensional microstructures through gradient-based optimization

“…In absence of a training data set, the transfer learning approach from [14] becomes interesting, which has recently been extended to 3D [3]. It makes no assumptions regarding microstructure, but the descriptor is restricted to Gram matrices 2 . An extension to combine the approach with spatial two-point correlations is given in [2].…”

“…It makes no assumptions regarding microstructure, but the descriptor is restricted to Gram matrices 2 . An extension to combine the approach with spatial two-point correlations is given in [2]. Finally, extremely efficient reconstructions without training on a specific data set are also obtained by limiting the descriptor to the underlying random field [8].…”

“…The distinct meaning of these variables cannot be directly determined as it results from the chosen architecture and the training process. 2 With the activation of the -th channel of a convolutional neural network in layer at the spatial position denoted as , the Gram matrix of layer is expressed as = ∑ .…”