Kipton Barros

Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

Abstract Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU ( 3 ) gauge field. Using NVIDIAs CUDA platform we have implemented a Wilson–Dirac sparse matrix–vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIAs GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Dielectric effects in the self-assembly of binary colloidal aggregates

Electrostatic interactions play an important role in numerous self-assembly phenomena, including colloidal aggregation. Although colloids typically have a dielectric constant that differs from the surrounding solvent, the effective interactions that arise from inhomogeneous polarization charge distributions are generally neglected in theoretical and computational studies. We introduce an efficient technique to resolve polarization charges in dynamical dielectric geometries, and demonstrate that dielectric effects qualitatively alter the predicted self-assembled structures, with surprising colloidal strings arising from many-body effects.

Efficient and accurate simulation of dynamic dielectric objects

Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface bound charge from a matrix equation using the Generalized Minimal Residue method (GMRES). Empirically, we find that GMRES converges very quickly. Indeed, our detailed analysis suggests that the relevant matrix has a very compact spectrum for all non-degenerate dielectric geometries. Each GMRES iteration can be evaluated using a fast Ewald solver with cost that scales linearly or near-linearly in the number of surface charge elements. We analyze several previously proposed methods for calculating the bound charge, and show that our approach compares favorably.

Learning molecular energies using localized graph kernels

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Comparison of efficient techniques for the simulation of dielectric objects in electrolytes

We review two recently developed efficient approaches for the numerical evaluation of the electrostatic polarization potential in particle-based simulations. The first is an image-charge method that can be applied to systems of spherical dielectric objects and provides a closed-form solution of Poissons equation through multiple image-charge reflections and numerical evaluation of the resulting line integrals. The second is a boundary-element method that computes the discretized surface bound charge through a combination of the generalized minimal residual method (GMRES) and a fast Ewald solver. We compare the accuracy and efficiency of both approaches as a function of the pertinent numerical parameters. We demonstrate use of the image-charge method in a Monte Carlo simulation using the Barnes-Hut octree algorithm and the boundary-element method in a molecular dynamics simulation using the Particle-Particle Particle-Mesh (PPPM) Ewald method, and present numerical results for the ensemble-averaged induced force between two spherical colloids immersed in an electrolyte.

Hierarchical modeling of molecular energies using a deep neural network

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over hierarchical terms. These terms are generated from a neural network-a composition of many nonlinear transformations-acting on a representation of the molecule. HIP-NN achieves the state-of-the-art performance on a dataset of 131k ground state organic molecules and predicts energies with 0.26 kcal/mol mean absolute error. With minimal tuning, our model is also competitive on a dataset of molecular dynamics trajectories. In addition to enabling accurate energy predictions, the hierarchical structure of HIP-NN helps to identify regions of model uncertainty.

Optimisation of GaN LEDs and the reduction of efficiency droop using active machine learning.

A fundamental challenge in the design of LEDs is to maximise electro-luminescence efficiency at high current densities. We simulate GaN-based LED structures that delay the onset of efficiency droop by spreading carrier concentrations evenly across the active region. Statistical analysis and machine learning effectively guide the selection of the next LED structure to be examined based upon its expected efficiency as well as model uncertainty. This active learning strategy rapidly constructs a model that predicts Poisson-Schrödinger simulations of devices, and that simultaneously produces structures with higher simulated efficiencies.

Spatial adaptive sampling in multiscale simulation

Abstract In a common approach to multiscale simulation, an incomplete set of macroscale equations must be supplemented with constitutive data provided by fine-scale simulation. Collecting statistics from these fine-scale simulations is typically the overwhelming computational cost. We reduce this cost by interpolating the results of fine-scale simulation over the spatial domain of the macro-solver. Unlike previous adaptive sampling strategies, we do not interpolate on the potentially very high dimensional space of inputs to the fine-scale simulation. Our approach is local in space and time, avoids the need for a central database, and is designed to parallelize well on large computer clusters. To demonstrate our method, we simulate one-dimensional elastodynamic shock propagation using the Heterogeneous Multiscale Method (HMM); we find that spatial adaptive sampling requires only ≈ 50 × N 0.14 fine-scale simulations to reconstruct the stress field at all N grid points. Related multiscale approaches, such as Equation Free methods, may also benefit from spatial adaptive sampling.

Distributed Database Kriging for Adaptive Sampling (D2KAS)

Abstract We present an adaptive sampling method supplemented by a distributed database and a prediction method for multiscale simulations using the Heterogeneous Multiscale Method. A finite-volume scheme integrates the macro-scale conservation laws for elastodynamics, which are closed by momentum and energy fluxes evaluated at the micro-scale. In the original approach, molecular dynamics (MD) simulations are launched for every macro-scale volume element. Our adaptive sampling scheme replaces a large fraction of costly micro-scale MD simulations with fast table lookup and prediction. The cloud database Redis provides the plain table lookup, and with locality aware hashing we gather input data for our prediction scheme. For the latter we use kriging, which estimates an unknown value and its uncertainty (error) at a specific location in parameter space by using weighted averages of the neighboring points. We find that our adaptive scheme significantly improves simulation performance by a factor of 2.5–25, while retaining high accuracy for various choices of the algorithm parameters.

Magnetic-field-induced phases in anisotropic triangular antiferromagnets: Application toCuCrO2

We introduce a minimal spin model for describing the magnetic properties of