Physics based supervised and unsupervised learning of graph structure

Graphs are central tools to aid our understanding of biological, physical, and social systems. Graphs also play a key role in representing and understanding the visual world around us, 3D-shapes and 2D-images alike. In this dissertation, I propose the use of physical or natural phenomenon to understand graph structure. I investigate four phenomenon or laws in nature: (1) Brownian motion, (2) Gauss\u27s law, (3) feedback loops, and (3) neural synapses, to discover patterns in graphs

SurfNet: Generating 3D shape surfaces using deep residual networks

3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a voxelized representation of the object. Lifting convolution operators from the traditional 2D to 3D results in high computational overhead with little additional benefit as most of the geometry information is contained on the surface boundary. Here we study the problem of directly generating the 3D shape surface of rigid and non-rigid shapes using deep convolutional neural networks. We develop a procedure to create consistent `geometry images' representing the shape surface of a category of 3D objects. We then use this consistent representation for category-specific shape surface generation from a parametric representation or an image by developing novel extensions of deep residual networks for the task of geometry image generation. Our experiments indicate that our network learns a meaningful representation of shape surfaces allowing it to interpolate between shape orientations and poses, invent new shape surfaces and reconstruct 3D shape surfaces from previously unseen images.Comment: CVPR 2017 pape

Magnetotransport properties of a twisted bilayer graphene in the presence of external electric and magnetic field

We extensively investigate the electronic and transport properties of a twisted bilayer graphene when subjected to both an external perpendicular electric field and a magnetic field. Using a basic tight-binding model, we show the flat electronic band properties as well as the density of states (DOS), both without and with the applied electric field. In the presence of an electric field, the degeneracy at the Dirac points is lifted where the non-monotonic behavior of the energy gap exists, especially for twist angles below 3$^\circ$. We also study the behavior of the Landau levels (LL) spectra for different twist angles within a very low energy range. These LL spectra get modified under the influence of the external electric field. Moreover, we calculate the dc Hall conductivity ($\sigma_{xy}$) for a very large system using the Kernel Polynomial Method (KPM). Interestingly, $\sigma_{xy}$ makes a transition from a half-integer to an integer quantum Hall effect, \textit{i.e.} the value of $\sigma_{xy}$ shifts from $\pm 4(n+1/2) (2e^2/h)$ ($n$ is an integer) to $\pm 2n (2e^2/h)$ around a small twist angle of $\theta=2.005^\circ$. At this angle, $\sigma_{xy}$ acquires a Hall plateau at zero Fermi energy. However, the behavior of $\sigma_{xy}$ remains unaltered when the system is exposed to the electric field, particularly at the magic angle where the bands in both layers can hybridize and strong interlayer coupling plays a crucial role.Comment: 13 pages, 10 figure

Imaging through glass diffusers using densely connected convolutional networks

Computational imaging through scatter generally is accomplished by first characterizing the scattering medium so that its forward operator is obtained and then imposing additional priors in the form of regularizers on the reconstruction functional to improve the condition of the originally ill-posed inverse problem. In the functional, the forward operator and regularizer must be entered explicitly or parametrically (e.g., scattering matrices and dictionaries, respectively). However, the process of determining these representations is often incomplete, prone to errors, or infeasible. Recently, deep learning architectures have been proposed to instead learn both the forward operator and regularizer through examples. Here, we propose for the first time, to our knowledge, a convolutional neural network architecture called “IDiffNet” for the problem of imaging through diffuse media and demonstrate that IDiffNet has superior generalization capability through extensive tests with well-calibrated diffusers. We also introduce the negative Pearson correlation coefficient (NPCC) loss function for neural net training and show that the NPCC is more appropriate for spatially sparse objects and strong scattering conditions. Our results show that the convolutional architecture is robust to the choice of prior, as demonstrated by the use of multiple training and testing object databases, and capable of achieving higher space–bandwidth product reconstructions than previously reported.Singapore-MIT AllianceUnited States. Office of the Director of National Intelligence. Rapid Analysis of Various Emerging NanoelectronicsUnited States. Department of Energy (DE-FG02-97ER25308)United States. Department of Energy. Computational Science Graduate Fellowship Progra

Comparative analysis of the stock markets of China, Russia, Brazil, South Africa and Argentina

In this study that we are conducting, the end goal is to undertake a comparative analysis of the stock markets of Russia, China, South Africa, Argentina and Brazil

Uncertainty management in the design of multiscale systems

In this thesis, a framework is laid for holistic uncertainty management for simulation-based design of multiscale systems. The work is founded on uncertainty management for microstructure mediated design (MMD) of material and product, which is a representative example of a system over multiple length and time scales, i.e., a multiscale system. The characteristics and challenges for uncertainty management for multiscale systems are introduced context of integrated material and product design. This integrated approach results in different kinds of uncertainty, i.e., natural uncertainty (NU), model parameter uncertainty (MPU), model structure uncertainty (MSU) and propagated uncertainty (PU). We use the Inductive Design Exploration Method to reach feasible sets of robust solutions against MPU, NU and PU. MMD of material and product is performed for the product autonomous underwater vehicle (AUV) employing the material in-situ metal matrix composites using IDEM to identify robust ranged solution sets. The multiscale system results in decision nodes for MSU consideration at hierarchical levels, termed as multilevel design. The effectiveness of using game theory to model strategic interaction between the different levels to facilitate decision making for mitigating MSU in multilevel design is illustrated using the compromise decision support problem (cDSP) technique. Information economics is identified as a research gap to address holistic uncertainty management in simulation-based multiscale systems, i.e., to address the reduction or mitigation of uncertainty considering the current design decision and scope for further simulation model refinement in order to reach better robust solutions. It necessitates development of an improvement potential (IP) metric based on value of information which suggests the scope of improvement in a designer's decision making ability against modeled uncertainty (MPU) in simulation models in multilevel design problem. To address the research gap, the integration of robust design (using IDEM), information economics (using IP) and game theoretic constructs (using cDSP) is proposed. Metamodeling techniques and expected value of information are critically reviewed to facilitate efficient integration. Robust design using IDEM and cDSP are integrated to improve MMD of material and product and address all four types of uncertainty simultaneously. Further, IDEM, cDSP and IP are integrated to assist system level designers in allocating resources for simulation model refinement in order to satisfy performance and robust process requirements. The approach for managing MPU, MSU, NU and PU while mitigating MPU is presented using the MMD of material and product. The approach presented in this article can be utilized by system level designers for managing all four types of uncertainty and reducing model parameter uncertainty in any multiscale system.M.S.Committee Chair: Dr. Janet K. Allen; Committee Co-Chair: Dr. Farrokh Mistree; Committee Member: Dr. David Rosen; Committee Member: Dr. Jitesh H. Pancha