LANS Informal Seminar: LANS Summer Students

Seminar Title: SASSy – Part 2
Speaker: LANS Summer Students,

Date/Time: 2015-08-07 13:00
Location: Building 240 rm 1404-1405

Description:
Speaker list:
1:00 PM Andres Alvarez Elia Merzarii, Oana Marin
1:15 PM Annie Goering Paul Fischer
1:30 PM Bo Han Sven Leyffer
1:45 PM Li Lu Paul Fischer

2:00 PM BREAK

2:15 PM Matt Menickelly Stefan Wild
2:30 PM Pelin Cay Sven Leyffer
2:45 PM Jing Yu Mihai Anitescu

3:00 PM BREAK

3:15 PM Matt Otten Mi Sun Min
3:30 PM Ahmed Attia Emil Constantinescu
3:45 PM Sean Shahkarami Barry Smith

Abstracts:

Session 3 1:00-2:00 PM
Session Chair: Jeff Larson

1:00-1:15 PM
Student: Andres Alvarez
Title: Proper Orthogonal Analysis of the MAX Experiment
Abstract: In a sodium cooled fast reactor thermal striping – temperature fluctuations produced from convective mixing- is a significant safety concern. The MAX project explores the effects of thermal striping through both experimentation and simulation. A proper orthogonal decomposition (POD) analysis was conducted on the MAX experiment geometry in order gain a deeper physical understanding of thermal striping.

1:15-1:30 PM
Student: Annie Goering
Title: Building Block Simulations with Nek5000
Abstract: Nek5000 is an open source computational fluid dynamics solver. It implements spectral element analysis to solve incompressible flow problems. Presented with an opportunity to demonstrate Nek5000?s large scale application from industry, a building block model is being developed. By generating a series of small scale meshes and utilizing the pre-processor and Nek5000 to solve for pressure and velocity fields; large meshes and domains can be simulated by feeding variables from each building block into another. Development is underway for a complete small scale set.

1:30-1:45 PM
Student: Bo Han
Title: Phase Retrieval Problem via PhaseLifting
Abstract: Phase Retrieval is known as a problem of recovering a general signal from the magnitude of its Fourier transformation. Several algorithms, such as hybrid input output, error reduction, with good empirical performance have been developed. However, due to non-convexity, these algorithms can stall in local minima. Then, PhaseLifting is introduced as a novel methodology to solve phase retrieval by relaxing the nonconvex problem into a convex program by applying classical lifting argument for nonconvex quadratic programs and semidefinite programming relaxation. In this talk, we will present the semidefinite programming relaxation of the problem and some preliminary numerical results to illustrate how it is used to affect the results.

1:45-2:00 PM
Student: Li Lu
Title: A compressible flow solver using discontinuous Galerkin methods in Nek5000
Abstract: Nek5000 is an open-source computational fluid dynamics (CFD) solver. At its core is spectral element methods designed for incompressible flow equations. Its high-order accuracy and great scalability make it suitable and in fact widely used in large-scale 3D turbulent flow simulations. By devoting efforts into developing a discontinuous Galerkin methods sovler for Nek5000, we aim to not only broaden Nek’s application to include compressible flow problems, but also make use of the property of less communication for discontinuous Galerkin methods to make our code even more parallel-efficient. Discontinuous Galerkin methods differ from the normal Galerkin methods commonly used in finite element methods in the sense that they no longer require coninuity across element interfaces for flow variables such as density and momentum; instead, they rely on cleverly designed numerical flux schemes to ensure laws of conservation. This relaxed constraint gives promises on shock-capturing, which is beyond traditional Galerkin methods.

BREAK 2:00-2:15 PM

Session 4 2:15-3:15 PM
Session Chair: Julie Bessac

2:15-2:30 PM
Student: Matt Menickelly
Title: Manifold Sampling for Greybox” Optimization
Abstract: We consider the minimization of a nonsmooth function of simulation outputs. While the simulation outputs are black boxes, we assume that the nonsmooth function is known (e.g. a sum of absolute values or a pointwise maximum). Borrowing ideas from the approach of gradient sampling, we propose a method for solving problems of this greybox type which we call ”manifold sampling”, an extension of model-based trust-region methods for derivative-free optimization. Given that the nonsmooth function satisfies some fairly typical assumptions, we prove that the cluster points generated by our iterative method are stationary in the Clarke sense. We also give some preliminary numerical results where the nonsmooth function is the L1 norm of the vector of simulation outputs.

2:30-2:45 PM
Student: Pelin Cay
Title: Mixed-Integer PDE-Constrained Optimization
Abstract: Mixed-Integer PDE-Constrained Optimization (MIPDECO) is focusing on a new class of optimization problems that include constraints with partial differential equations (PDEs) and some of the decision variables as integers. These problems have a broad application area such as in maximizing oil recovery problem and control of the gas network problems. In these problems, both the combinatorial challenge of the integer decision variables and the computational complexity of PDE constrained optimization problems are in single problem. In this study, we worked on introducing a benchmark set of these problems. We implemented mixed integer programming (MIP) – based prototyping that we discretize the PDE and solve the resulting nonlinear MIP problem. We present some preliminary numerical results that highlight the challenges of this new class of problems.

2:45-3:00 PM
Student: Jing Yu
Title: An Application of A-Optimal Design for Sensor Placement
Abstract: When monitoring spatial phenomena, choosing sensor locations is a fundamental task. There are several strategies to address this experimental design problem. One choice is A-optimal design, which is to minimize the uncertainty in the parameters from a Bayesian linear inverse problem governed by partial differential equations (PDEs). In this talk, we present an application of A-optimal design for sensor placement in the natural gas pipeline network, where the governing PDEs are hyperbolic. First we consider the one-wave equation case, where the uncertainty is measured by the trace of posterior covariance matrix. Then we tackle the two-variable problem, which involves pressure and mass flow in the gas system, and the uncertainty is measured by the variance of total flow. We exploit matrix sparsity to alleviate the computational cost in both cases and demonstrate the sparsified experimental designs.

BREAK 3:00-3:15 PM

Session 5 3:15-4:00 PM
Session Chair: Wendy Di

3:15-3:30 PM
Student: Matt Otten
Title: GPU Accelerated Quantum Physics Calculations
Abstract: We study the time dynamics of open quantum systems, including nanoscale and quantum computing systems, using the density matrix formalism. The size of the density matrix grows quickly; a physically reasonable system of 16 quantum dots requires a matrix dimension of $50*2^16$. At this size, extreme scale computing must be utilized. We’ve worked on implementing a scalable communication library for many different architectures, focusing mostly on GPU programming using OpenACC. We show results from the physical systems, describe the communication algorithm, and show results from NEKCEM running on the Titan.

3:30-3:45 PM
Student: Ahmed Attia
Title: PyDA: A Python Package for Sequential Data Assimilation
Abstract: Data assimilation (DA) combines information from models, measurements, and priors to obtain improved estimates of the state of a dynamical system such as the atmosphere. Ensemble-based DA schemes, such as the Ensemble Kalman filter (EnKF), generate ensembles of states obtained from the posterior distribution. Most of these algorithms are derived under the assumption that the underlying probability distributions are Gaussian. An efficient solution of the non-Gaussian DA requires generating a small number of states, sampled from a complicated posterior, that can cover all the high-probability regions (HPRs) with representative mass distribution. Hybrid/Hamiltonian Monte-Carlo (HMC) is a promising sampling scheme that was recently proposed as a sequential filter as well as a smoother to solve the non-Gaussian DA problem. Comparing the performance of new schemes to existing algorithms is usually a challenging task due to lack of open-source DA testing suites. A unified testing suite written in a modern language would be very useful if it enables researchers to plug-in new models and new filters easily. We first present PyDA, a DA package written in Python. We designed PyDA in a way that makes it very straight forward to add new models and filters, and enables researchers to compare the performance of new methods to the popular algorithms such as EnKF. Currently PyDA supports sequential filters, but it can be easily extended to the four dimensional (smoothing) case. HMC for sequential non-Gaussian DA is then presented with a discussion of it’s limitations, and if time permits, a brief discussion of our ongoing attempt to handle these limitations.Finally, assimilation results obtained using several models such as Lorenz-96 and shallow water equations are presented and discussed.

3:45-4:00 PM
Student: Sean Shahkarami
Title: New Foundations for Water Management
Abstract: The main goal of this project is to develop a network-based platform for flexible and scalable watershed simulation. To achieve this goal, we’ve chosen PETSc’s DMNetwork component as the foundation for our implementation. In this talk, I’ll give a brief overview of the steps we’ve taken towards this goal.”