A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation

A software platform for global optimisation, called PaGMO, has been developed within the Advanced Concepts Team (ACT) at the European Space Agency, and was recently released as an open-source project. PaGMO is built to tackle high-dimensional global optimisation problems, and it has been successfully used to find solutions to real-life engineering problems among which the preliminary design of interplanetary spacecraft trajectories - both chemical (including multiple flybys and deep-space maneuvers) and low-thrust (limited, at the moment, to single phase trajectories), the inverse design of nano-structured radiators and the design of non-reactive controllers for planetary rovers. Featuring an arsenal of global and local optimisation algorithms (including genetic algorithms, differential evolution, simulated annealing, particle swarm optimisation, compass search, improved harmony search, and various interfaces to libraries for local optimisation such as SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs an object-oriented architecture providing a clean and easily-extensible optimisation framework. Adoption of multi-threaded programming ensures the efficient exploitation of modern multi-core architectures and allows for a straightforward implementation of the island model paradigm, in which multiple populations of candidate solutions asynchronously exchange information in order to speed-up and improve the optimisation process. In addition to the C++ interface, PaGMO's capabilities are exposed to the high-level language Python, so that it is possible to easily use PaGMO in an interactive session and take advantage of the numerous scientific Python libraries available.Comment: To be presented at 'ICATT 2010: International Conference on Astrodynamics Tools and Techniques

Parallel continuation-based global optimization for molecular conformation and protein folding

This paper presents the authors` recent work on developing parallel algorithms and software for solving the global minimization problem for molecular conformation, especially protein folding. Global minimization problems are difficult to solve when the objective functions have many local minimizers, such as the energy functions for protein folding. In their approach, to avoid directly minimizing a ``difficult`` function, a special integral transformation is introduced to transform the function into a class of gradually deformed, but ``smoother`` or ``easier`` functions. An optimization procedure is then applied to the new functions successively, to trace their solutions back to the original function. The method can be applied to a large class of nonlinear partially separable functions including energy functions for molecular conformation and protein folding. Mathematical theory for the method, as a special continuation approach to global optimization, is established. Algorithms with different solution tracing strategies are developed. Different levels of parallelism are exploited for the implementation of the algorithms on massively parallel architectures

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd

Molecular dynamics beyonds the limits: massive scaling on 72 racks of a BlueGene/P and supercooled glass transition of a 1 billion particles system

We report scaling results on the world's largest supercomputer of our recently developed Billions-Body Molecular Dynamics (BBMD) package, which was especially designed for massively parallel simulations of the atomic dynamics in structural glasses and amorphous materials. The code was able to scale up to 72 racks of an IBM BlueGene/P, with a measured 89% efficiency for a system with 100 billion particles. The code speed, with less than 0.14 seconds per iteration in the case of 1 billion particles, paves the way to the study of billion-body structural glasses with a resolution increase of two orders of magnitude with respect to the largest simulation ever reported. We demonstrate the effectiveness of our code by studying the liquid-glass transition of an exceptionally large system made by a binary mixture of 1 billion particles.Comment: 14 pages, 8 figures, submitted to Journal of Computational Physic

A KIM-compliant potfit for fitting sloppy interatomic potentials : application to the EDIP model for silicon

Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models Project). This makes it possible to use potfit to fit many KIM potential models, not just those prebuilt into the potfit code. Second, we incorporated the geodesic Levenberg–Marquardt (LM) minimization algorithm into potfit as a new local minimization algorithm. The extended potfit was tested by generating a training set using the KIM Environment-Dependent Interatomic Potential (EDIP) model for silicon and using potfit to recover the potential parameters from different initial guesses. The results show that EDIP is a “sloppy model” in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two-dimensional materials. The code is available for download via https://www.potfit.net