LANS Informal Seminar: Various Speakers

Seminar Title: LANS SASSy – Summer Argonne Students’ Symposium 2017 – PART II
Speaker: Various Speakers, Summer Students in LANS (MCS Division)

Date/Time: 2017-08-02 9:30
Location: Bldg. 240, 1406 & 1407

Description:
Session I
Chair: Matt Menickelly

Yu, Yiming 9:30AM
Title: Solving multi-objective optimization problems using generative adversarial networks
Abstract: Our goal is to find the Pareto optimal solution of multi-objective optimization problems using machine learning. We use generative adversarial networks (GANs) to learn the mapping of the inverse problems and use this mapping to solve for the Pareto optimal solution of the multi-objective optimization problem. We implement two extended versions of GANs for a variety of test problems and compare their training costs and convergence. Simulations show that for inverse problems conditional GANs with a modified loss function performs better than the conditional GANs. This leads us to use the approximated inverse mapping learned from GANs to find the Pareto optimal solution.

Nandi, Shinjini 9:45AM
Title: On determining sparsity patterns using probing methods in Bayesian framework.
Abstract: The aim of this project is to investigate and improve on existing probabilistic methods to determine the sparsity patterns in matrices. The underlying concept involves sequentially updating the Bayesian probabilities associated with non-zero elements in the sparse matrix, subject to minimization of expected number of discrepancies between actual and estimated sparse matrix. Single probing methods based on this idea seek to sequentially determine a minimal number of vectors that identify the sparsity pattern. The bundle probing approach arbitrates a set of vector probes to be used simultaneously and determine the sparsity pattern using a minimum number of such sets. We analyze the methods suggested by Griewank and Mitev (2002) and suggest some improvements in choices of the initial probability matrix and in the bundle probing algorithm that determines the sparsity pattern using fewer number of probes.

Gilles, Marc 10:00AM
Title: An algorithm for 3-D ptychography
Abstract: Ptychography is an imaging method whereby a coherent beam is scanned across an object. It allows for imaging of namometer scale objects, such as cells. In this talk we describe an algorithm for reconstructing three dimensional objects from ptychographic measurements.

Denchfield, Adam 10:15AM
Title: Failures of the Finite Element Method in Modeling Superconductivity
Abstract: The Finite Element Method (FEM) is a way to numerically solve partial differential equations (PDEs), typically on domains too complex for simpler methods. An example of a problem with complex domains is that of superconductivity; superconductors can often have defects in the material. We model a superconductor using the Time-Dependent Ginzburg Landau (TDGL) equations. An FEM was implemented from the literature and found to fail in certain regimes of the parameters; this behavior was explored.

Khatri, Ratna 10:30AM
Title: Regularization in Tomographic Reconstruction
Abstract: Tomographic reconstruction is a non-invasive 2D/3D image recovery technique based on inversion of a sequence of 1D/2D projections arising from multiple angles. It is widely used at the Advanced Photon Source at Argonne National Lab for applications in diverse science fields ranging from material science/engineering to biology and physics. One way of solving this problem is via linear least squares optimization formulation assuming the experimental data follows a Gaussian distribution. Due to limited data, the problem is usually ill-conditioned (e.g., the projection operator is rank-deficient). Our goal is to narrow down the solution space by imposing prior constraints like sparsity and smoothness. We study regularization techniques like lasso, ridge and elastic net regression for tomographic reconstruction, and provide a performance comparison among different types of regularizers.

Break 10:45AM – 11:00AM

Session II
Chair: Sandeep Madireddy

Chandramoothy, Nisha 11:00AM
Title: Automatic Differentiation for Chaotic Sensitivity Analysis
Abstract: In chaotic dynamical systems, sensitivities of statistically stationary quantities of interest to design parameters cannot be computed from long-time evolution of tangent or adjoint sensitivities or through finite difference, since all three methods solve ill-conditioned initial value problems. Non-Intrusive Least Squares Shadowing [Ni and Wang 2017] is a promising new approach to this problem, wherein a shadowing perturbation direction is approximately computed, along which sensitivities remain bounded for all time. This talk focuses on applying automatic differentiation (AD) techniques to the NILSS algorithm. Numerical results for sensitivities computed through the NILSS-AD package are presented for the Lorenz’63 system and a Rijke tube combustion model.

Chen, Yougrui (Richard) 11:15AM
Title: A Project on Scalable Statistical Algorithms for Large-Scale Gaussian Processes
Abstract: Many statistical applications require computing Gaussian likelihoods involving large covariance matrices, for examples, high-frequency time series inference and large-scale spatial modeling via Gaussian processes. Generally, these applications result in large dense covariance matrices that are prohibitively expensive in both computing and storage. Common numerical algorithms rely on Cholesky decomposition to compute the solve and determinant of a covariance matrix, e.g. the Scikit-learn library in Python, but it can not scale up to extremely large data set. By exploiting the structure of large dense matrices arising from stationary time series or spatial data, we implement a model-free approach to reduce both the computing and storage costs via a randomized algorithm, which only needs O(n) storage and O(nln(n)) computation. This approach utilizes circulant embedding for Toeplitz systems, fast Fourier transforms, circulant preconditioner, and conjugate gradient to enable a nearly linear scalability for spatial data on regular grids. We also discuss modifications for irregular grids including a technique for HODLR (hierarchical off-diagonal low-rank) matrices, and compare with an inverse-free estimating equation approach. Lastly, we show the result using our new algorithm on NASA’s Ozone data (OMI OMTO3d V3).

Venkit, Abishek 11:30AM
Title: Simulating Ultra-Thin Metalenses
Abstract: A conventional lens uses a curved surface to refract and focus light. Flat metalenses instead use millions of Huygens nanoresonators to shift the phase of light and focus it. This reduces lens thickness from millimeters to nanometers, which eliminates bulk and weight in optical devices while decreasing material costs. As interest in metalenses grows, optimization of lens geometry has become essential in improving efficiency. Using the spectral-element, discontinuous-Galerkin solver for time-dependent Maxwell equations, NekCEM, we aim to simulate metalenses and provide insight on how varying lens parameters improves efficiency.

Fu, Deqing 11:45AM
Title: ADOL-C Performance Benchmark and Application
Abstract: ADOL-C (Automatic Differentiation Overloading In C) is the technique to compute derivatives of function and is commonly used to compute gradients, jacobians and hessians. ADOL-C has been wrapped into python using SWIG and my job is to apply ADOL-C to a test suite of python functions to benchmark the efficiency of ADOL-C. The functions are both implemented in python and in numpy. The benchmarking part is to implement with ADOL-C methods to calculate the gradient of each function and to measure the time elapsed of both python and numpy implementations. The second part of my job is to apply ADOL-C to some machine learning codes such as one implemented with the method of LSTM-RNN. The third part is to re-implement functions in the python test suite using numba and to benchmark the performance of them comparing to python and numpy.