Summer Argonne Students Symposium (SASSy) Part II
Scalable Density Matrix Calculations of Coupled Quantum Systems
1:00 p.m. - 1:15 p.m.
Matt Otten (Supervisor: Misun Min)
We study the time dynamics of a system consisting of quantum dots coupled to a single plasmon mode. 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. Aside from the novel physics applications, we are currently studying how best to treat this system, through different time stepping schemes (RK and exponential time integrator) and different parallelization algorithms.
On Bilevel Mixed-Integer Nonlinear Programming Problems
1:15 p.m. - 1:30 p.m.
Harikrishnan Sreekumaran (Supervisor: Sven Leyffer)
Bilevel programming provides a natural framework for modelling hierarchical decision making, with applications in varied fields such as market design, network planning and vulnerability analysis, and engineering design among others. In this talk, we review bilevel mixed integer nonlinear programming problems (BLMINLPs) and describe the significant challenges in the analysis and algorithm design for such problems. We present relaxation formulations for certain classes of BLMINLPs and introduce algorithms for solving such problems using these relaxations. Finally we present a few application examples and some preliminary numerical results.
Building an Adjoint Based Dynamics Constrained Optimization of Electrical Power Systems
1:30 p.m. - 1:45 p.m.
Paul Tranquilli (Supervisor: Cosmin Petra)
We present a mathematical framework for the solution of optimal power flow, including dynamic security constraints, using adjoint based sensitivities. We briefly discuss some implementation details of using PETSc to perform both the forward and backward time integrations.
Automatic Discretization of ODE and PDE Systems Using Pyomo
1:45 p.m.- 2:00 p.m.
Bethany Nicholson (Supervisor: Victor Zavala)
Dynamic optimization problems that include ordinary/partial differential equations as constraints are typically solved by discretizing the model and then solving the resulting nonlinear problem. This talk introduces a way to do model discretization automatically using the open-source modeling language Pyomo. We will discuss the straight-forward syntax behind this new functionality as well as the flexible discretization options that are available. Finally, we will look at a couple sample problems that show the wide range of dynamic optimzation problems that can now be represented and solved using Pyomo.
Derivative-based Solution of the Constrained Optimization Problem(s) in DeMarco's Model
2:00 p.m. - 2:15 p.m.
Ahmed Attia (Supervisor: Mihai Anitescu)
Predicting cascading network failure is a vital problem for the ever increasing scale of engineered systems as electric power grids, communication networks, and internet. To predict cascading failures, for one or more branches, the bottleneck is a constrained optimization step. Without derivative information, this optimization step takes a very long time even for the simplest settings, and may even fail to converge for large simulation times. We considered a simple, but general, model developed by DeMarco to understand how small-scale failures of individual elements may propagate to produce global failures. My main task was to derive and implement the adjoint of the quadratic constraint(s). The derivative information of the cost functional and constraints, made the optimization very fast (roughly 100-150 times faster). The results are being extended now to large-scale settings.
Bound Contraction Algorithm for Global Optimization of Natural Gas Networks
2:15 p.m. - 2:30 p.m.
Francisco Trespalacios-Sagues (Supervisor: Victor Zavala)
The natural gas transportation network problem has received increased attention in recent years. In this work, we first derive a convex NLP for this problem, based on a well-known non-convex NLP and two operating assumptions. We then present a non-convex model that includes the cost of both: purchasing natural gas from suppliers, and operating compressors in the network. Finally, we develop a bound contraction algorithm to solve this non-convex model. The algorithm is tested in a simplified real network, and compared against state of the art global solvers.
2:30 p.m. - 2:45 p.m. Break
Handling Nonsmoothness in Derivative Free Optimization
2:45 p.m. - 3:00 p.m.
Matt Menickelly (Supervisor: Stefan Wild)
Derivative-free optimization is a branch of optimization theory concerned with optimizing functions for which derivatives are either unavailable (e.g. the objective is a black box) or are unreliable due to noise. A popular class of algorithms for derivative-free optimization is that of trust-region methods, wherein at each iteration, the objective is modeled locally using an interpolating function with respect to a choice of basis - in the scope of this research, and as is a common choice, a basis of quadratic polynomials. However, as one might expect, if there is nonsmoothness inherent in the objective, the failure of this basis to produce accurate local models of "kinks" or "corners" will cause a trust-region algorithm to stall. In this research, we explore the idea of approximate gradient sampling and the notion of convergence to Clarke stationarity to develop a mechanism to save trust-region methods from stalling as a result of nonsmoothness.
Approximation and Multilevel Algorithms for Phase Retrieval
3:00 p.m. - 3:15 p.m.
Cullen Tanoue (Supervisor: Sven Leyffer)
Phase retrieval poses an important optimization problem that arises in diffraction imaging, where the original structure of an object needs to be reconstructed from its diffraction data with loss of information concerning the phase of the object. Multilevel algorithms can be used to compute solutions to the standard phase retrieval optimization problem by constructing a hierarchy of problems using a series of restriction and prolongation operations. The coarser problems have a quarter of the variables as the finer problems, and hence, there are much less linear algebra requirements for solving the coarser problems. Further, the prolongation of the solutions computed for the coarser problems yield good starting points for the finer problems. We can also use an approach that alternates between solving the coarse and fine problem. Parameters for these methods include the number of levels, prolongation and restriction operations, and the number of iterations to perform at each level. We study the solutions to the standard phase retrieval optimization problem that result from exploring these parameters.
Finding Particles in Halos: Resolving Local Effects when Simulating DNA Molecules
3:15 p.m. - 3:30 p.m.
Matthew Michelotti (Supervisor: Barry Smith)
Understanding how DNA molecules behave in a liquid is important for improving DNA sequencers. We can model DNA molecules as strings of charged particles. Using the GGEM method, each particle needs to receive information from other nearby particles in its "halo" to resolve local effects. We have added functionality to the libMesh library for having particles in a mesh and for finding particles in halos efficiently, in serial or parallel, for use with GGEM and similar methods.
Development of a User Controlled Threading Model for PETSc
3:30 p.m. - 3:45 p.m.
Paul Eller (Supervisor: Barry Smith)
In recent years multicore processors have become more common and hybrid programming models have been used to produce better performance than pure MPI in some situations. Therefore we have been working to develop a hybrid programming model for PETSc that allows users to take advantage of both MPI and threads. Multiple threaded programming models are being implemented in PETSc including models that give users more direct control of the threads. A threaded programming model introduces thread safety issues to PETSc which require non-trivial changes to routines throughout PETSc to ensure that the code produces accurate solutions without reducing performance.
Improving low memory state estimation of weakly constrained 4D-Var with gradient evaluation
3:45 p.m. - 4:00 p.m.
Wanting Xu (Supervisor: Mihai Anitescu)
Data assimilation is the process of estimating the states of a dynamical system with observation data. The underlying states and observables form a hidden Markov model, and the best states can be obtained by minimizing a corresponding likelihood function. We developed a recursive scheme for evaluating the gradient of the object function in a low memory fashion, and use that information in optimization. We demonstrate the improvement of our method over the existing low memory approach by simulation with Burgers' Equation and a linear PDE.
Web Interface for Parallel Linear Solver Selection
4:00 p.m. - 4:15 p.m.
Surtai Han (Supervisor: Barry Smith)
PETSc (Portable Extensible Toolkit for Scientific Computation) has a large selection of linear solvers to provide users with tools for a wide range of applications on parallel computers. However, it can be difficult for users to select the optimal solvers for their specific application. We built a webpage to assist users in viewing, customizing, and assembling the linear solvers by providing a GUI consisting of a hierarchy of drop-down menus and a tree diagram. Afterwards, the webpage generates the appropriate command-line options for the solvers that the user selected. A separate webpage allows users to interact with the SAWs (Scientific Applications Web Server) so that users can adjust the solver options during runtime.