arXiv subjects

Jonghyun Lee

Publications and source records attributed to Jonghyun Lee.

44 records · Page 3Linked to original sources

arXiv2021

PBBFMM3D: a parallel black-box algorithm for kernel matrix-vector multiplication

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably requires $O(N)$ operations to reduce the computation cost. The distinct feature of our method is that it requires only the ability to evaluate the kernel function, offering a black-box interface to users. Our parallel approach targets multi-core shared-memory machines and is implemented using OpenMP. Numerical results demonstrate up to $19\times$ speedup on 32 cores. We also present a real-world application in geostatistics, where our parallel method was used to deliver fast principle component analysis of covariance matrices.

cs.MS↗

arXiv2020

Application of deep learning to large scale riverine flow velocity estimation

Fast and reliable prediction of riverine flow velocities is important in many applications, including flood risk management. The shallow water equations (SWEs) are commonly used for prediction of the flow velocities. However, accurate and fast prediction with standard SWE solvers is challenging in many cases. Traditional approaches are computationally expensive and require high-resolution riverbed profile measurement ( bathymetry) for accurate predictions. As a result, they are a poor fit in situations where they need to be evaluated repetitively due, for example, to varying boundary condition (BC), or when the bathymetry is not known with certainty. In this work, we propose a two-stage process that tackles these issues. First, using the principal component geostatistical approach (PCGA) we estimate the probability density function of the bathymetry from flow velocity measurements, and then we use multiple machine learning algorithms to obtain a fast solver of the SWEs, given augmented realizations from the posterior bathymetry distribution and the prescribed range of BCs. The first step allows us to predict flow velocities without direct measurement of the bathymetry. Furthermore, the augmentation of the distribution in the second stage allows incorporation of the additional bathymetry information into the flow velocity prediction for improved accuracy and generalization, even if the bathymetry changes over time. Here, we use three solvers, referred to as PCA-DNN (principal component analysis-deep neural network), SE (supervised encoder), and SVE (supervised variational encoder), and validate them on a reach of the Savannah river near Augusta, GA. Our results show that the fast solvers are capable of predicting flow velocities with good accuracy, at a computational cost that is significantly lower than the cost of solving the full boundary value problem with traditional methods.

cs.LG↗

arXiv2020

Fast and Scalable Earth Texture Synthesis using Spatially Assembled Generative Adversarial Neural Networks

The earth texture with complex morphological geometry and compositions such as shale and carbonate rocks, is typically characterized with sparse field samples because of an expensive and time-consuming characterization process. Accordingly, generating arbitrary large size of the geological texture with similar topological structures at a low computation cost has become one of the key tasks for realistic geomaterial reconstruction. Recently, generative adversarial neural networks (GANs) have demonstrated a potential of synthesizing input textural images and creating equiprobable geomaterial images. However, the texture synthesis with the GANs framework is often limited by the computational cost and scalability of the output texture size. In this study, we proposed a spatially assembled GANs (SAGANs) that can generate output images of an arbitrary large size regardless of the size of training images with computational efficiency. The performance of the SAGANs was evaluated with two and three dimensional (2D and 3D) rock image samples widely used in geostatistical reconstruction of the earth texture. We demonstrate SAGANs can generate the arbitrary large size of statistical realizations with connectivity and structural properties similar to training images, and also can generate a variety of realizations even on a single training image. In addition, the computational time was significantly improved compared to standard GANs frameworks.

cs.CV↗

arXiv2020

iCaps: An Interpretable Classifier via Disentangled Capsule Networks

We propose an interpretable Capsule Network, iCaps, for image classification. A capsule is a group of neurons nested inside each layer, and the one in the last layer is called a class capsule, which is a vector whose norm indicates a predicted probability for the class. Using the class capsule, existing Capsule Networks already provide some level of interpretability. However, there are two limitations which degrade its interpretability: 1) the class capsule also includes classification-irrelevant information, and 2) entities represented by the class capsule overlap. In this work, we address these two limitations using a novel class-supervised disentanglement algorithm and an additional regularizer, respectively. Through quantitative and qualitative evaluations on three datasets, we demonstrate that the resulting classifier, iCaps, provides a prediction along with clear rationales behind it with no performance degradation.

cs.CV↗

arXiv2020

Algorithmic resolution via weighted blowings up

In this paper we describe a computer implementation of Abramovich, Temkin, and Wlodarczyk's algorithm for resolving singularities in characteristic zero. Their "weighted resolution" algorithm proceeds by repeatedly blowing up along centers that are independent of the history of the past blowing ups, distinguishing weighted resolution from previous resolution algorithms, which all rely on history. We compare our implementation of weighted resolution with that of Villamayor's resolution algorithm, experimentally verifying that weighted resolution is remarkably efficient.

math.AG↗

arXiv2020

Joint Contrastive Learning for Unsupervised Domain Adaptation

Enhancing feature transferability by matching marginal distributions has led to improvements in domain adaptation, although this is at the expense of feature discrimination. In particular, the ideal joint hypothesis error in the target error upper bound, which was previously considered to be minute, has been found to be significant, impairing its theoretical guarantee. In this paper, we propose an alternative upper bound on the target error that explicitly considers the joint error to render it more manageable. With the theoretical analysis, we suggest a joint optimization framework that combines the source and target domains. Further, we introduce Joint Contrastive Learning (JCL) to find class-level discriminative features, which is essential for minimizing the joint error. With a solid theoretical framework, JCL employs contrastive loss to maximize the mutual information between a feature and its label, which is equivalent to maximizing the Jensen-Shannon divergence between conditional distributions. Experiments on two real-world datasets demonstrate that JCL outperforms the state-of-the-art methods.

cs.CV↗

arXiv2020

Connectivity-informed Drainage Network Generation using Deep Convolution Generative Adversarial Networks

Stochastic network modeling is often limited by high computational costs to generate a large number of networks enough for meaningful statistical evaluation. In this study, Deep Convolutional Generative Adversarial Networks (DCGANs) were applied to quickly reproduce drainage networks from the already generated network samples without repetitive long modeling of the stochastic network model, Gibb's model. In particular, we developed a novel connectivity-informed method that converts the drainage network images to the directional information of flow on each node of the drainage network, and then transform it into multiple binary layers where the connectivity constraints between nodes in the drainage network are stored. DCGANs trained with three different types of training samples were compared; 1) original drainage network images, 2) their corresponding directional information only, and 3) the connectivity-informed directional information. Comparison of generated images demonstrated that the novel connectivity-informed method outperformed the other two methods by training DCGANs more effectively and better reproducing accurate drainage networks due to its compact representation of the network complexity and connectivity. This work highlights that DCGANs can be applicable for high contrast images common in earth and material sciences where the network, fractures, and other high contrast features are important.

physics.geo-ph↗

arXiv2015

Randomized algorithms for Generalized Hermitian Eigenvalue Problems with application to computing Karhunen-Loève expansion

We describe randomized algorithms for computing the dominant eigenmodes of the Generalized Hermitian Eigenvalue Problem (GHEP) $Ax=λBx$, with $A$ Hermitian and $B$ Hermitian and positive definite. The algorithms we describe only require forming operations $Ax$, $Bx$ and $B^{-1}x$ and avoid forming square-roots of $B$ (or operations of the form, $B^{1/2}x$ or $B^{-1/2}x$). We provide a convergence analysis and a posteriori error bounds that build upon the work of~\cite{halko2011finding,liberty2007randomized,martinsson2011randomized} (which have been derived for the case $B=I$). Additionally, we derive some new results that provide insight into the accuracy of the eigenvalue calculations. The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of $B^{-1}A$ decay rapidly. A randomized algorithm for the Generalized Singular Value Decomposition (GSVD) is also provided. Finally, we demonstrate the performance of our algorithm on computing the Karhunen-Loève expansion, which is a computationally intensive GHEP problem with rapidly decaying eigenvalues.

math.NA↗