Towards Microstructural State Variables in Materials Systems

The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large microstructural datasets. There is a need for machine learning techniques that can manage data complexity by capturing the maximal amount of information about the microstructure using the least number of variables. This paper aims to formulate dimensionality and state variable estimation techniques focused on reducing microstructural image data. It is shown that local dimensionality estimation based on nearest neighbors tend to give consistent dimension estimates for natural images for all p-Minkowski distances. However, it is found that dimensionality estimates have a systematic error for low-bit depth microstructural images. The use of Manhattan distance to alleviate this issue is demonstrated. It is also shown that stacked autoencoders can reconstruct the generator space of high dimensional microstructural data and provide a sparse set of state variables to fully describe the variability in material microstructures.

Machine learning in quantum computers via general Boltzmann Machines: Generative and Discriminative training through annealing

We present a Hybrid-Quantum-classical method for learning Boltzmann machines (BM) for generative and discriminative tasks. Boltzmann machines are undirected graphs that form the building block of many learning architectures such as Restricted Boltzmann machines (RBM's) and Deep Boltzmann machines (DBM's). They have a network of visible and hidden nodes where the former are used as the reading sites while the latter are used to manipulate the probability of the visible states. BM's are versatile machines that can be used for both learning distributions as a generative task as well as for performing classification or function approximation as a discriminative task. We show that minimizing KL-divergence works best for training BM for applications of function approximation. In our approach, we use Quantum annealers for sampling Boltzmann states. These states are used to approximate gradients in a stochastic gradient descent scheme. The approach is used to demonstrate logic circuits in the discriminative sense and a specialized two-phase distribution using generative BM.