Bayesian optimization for materials design

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality

COMPUTATIONAL TECHNIQUES FOR UNCERTAINTY MODELING AND STOCHASTIC OPTIMIZATION OF MATERIAL SYSTEMS

As applications of materials continue to increase in complexity, there is a clear need to quantitatively assess and optimize material performance in the presence of uncertainties. Insufficient knowledge of the physical phenomena at different length scales, the lack of understanding of the way information propagates from one length scale to another and the presence of inherent uncertainties leads to material response that cannot be accurately predicted using deterministic models. In this work, a novel computational framework for uncertainty modeling and design of complex systems is developed. In the first part of the thesis, computational tools for stochastic modeling of material systems is discussed. Probability distribution functions (PDFs) providing a complete representation of microstructural variability is discussed. We use the maximum entropy (MaxEnt) principle to compute a PDF of microstructures based on given information. Microstructural features are incorporated into the maximum entropy framework using data obtained from experiments or simulations. Microstructures are sampled from the computed MaxEnt PDF using concepts from Gibbs sampling, computational geometry and voronoi-cell tessellations. The MaxEnt technique is applied on a wide range of materials including multi-phase and polycrystalline structures. These microstructures are then interrogated in virtual deformation tests to compute the variability of non-linear stress-strain curve, elastic moduli as well as fracture-initiation stress. In the second half, we explore the design of material systems in the presence of uncertainties - both in input variables as well as design variables. The robust design problem is posed as a stochastic optimization problem. The concept of stochastic sensitivities is introduced and a stochastic gradient descent approach is proposed to compute the optimal solutions. The sparse grid stochastic collocation technique is utilized to accelerate computing the optimal stochastic solution. These techniques are used in conjunction with Finite Element techniques for the simulation of physical phenomenon in material systems. The technique is validated on stochastic inverse problems in thermal-diffusive systems and problems involving flow in porous media. Finally, examples on robust design for large-deformation processes is discussed and scope for future work are discussed.Army Research Office Air Force Office of Scientific Researc

Smart Water Resource Management Using Artificial Intelligence—A Review

Water management is one of the crucial topics discussed in most of the international forums. Water harvesting and recycling are the major requirements to meet the global upcoming demand of the water crisis, which is prevalent. To achieve this, we need more emphasis on water management techniques that are applied across various categories of the applications. Keeping in mind the population density index, there is a dire need to implement intelligent water management mechanisms for effective distribution, conservation and to maintain the water quality standards for various purposes. The prescribed work discusses about few major areas of applications that are required for efficient water management. Those are recent trends in wastewater recycle, water distribution, rainwater harvesting and irrigation management using various Artificial Intelligence (AI) models. The data acquired for these applications are purely unique and also differs by type. Hence, there is a dire need to use a model or algorithm that can be applied to provide solutions across all these applications. Artificial Intelligence (AI) and Deep Learning (DL) techniques along with the Internet of things (IoT) framework can facilitate in designing a smart water management system for sustainable water usage from natural resources. This work surveys various water management techniques and the use of AI/DL along with the IoT network and case studies, sample statistical analysis to develop an efficient water management framework