Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations

AbstractSimulation of in vivo cellular processes with the reaction–diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel efficiency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems

Deducing effective light transport parameters in optically thin systems

We present an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation. We completely characterize the so-called ballistic-to-diffusive transition, notably in terms of the spatial variance of the transmitted/reflected profile. We test the validity of the prediction cast by diffusion theory, that the spatial variance should grow independently of absorption and, to a first approximation, of the sample thickness and refractive index contrast. Based on a large set of simulated data, we build a freely available look-up table routine allowing reliable and precise determination of the microscopic transport parameters starting from robust observables which are independent of absolute intensity measurements. We also present the Monte Carlo software package that was developed for the purpose of this study

Simulation of 1+1 dimensional surface growth and lattices gases using GPUs

Restricted solid on solid surface growth models can be mapped onto binary lattice gases. We show that efficient simulation algorithms can be realized on GPUs either by CUDA or by OpenCL programming. We consider a deposition/evaporation model following Kardar-Parisi-Zhang growth in 1+1 dimensions related to the Asymmetric Simple Exclusion Process and show that for sizes, that fit into the shared memory of GPUs one can achieve the maximum parallelization speedup ~ x100 for a Quadro FX 5800 graphics card with respect to a single CPU of 2.67 GHz). This permits us to study the effect of quenched columnar disorder, requiring extremely long simulation times. We compare the CUDA realization with an OpenCL implementation designed for processor clusters via MPI. A two-lane traffic model with randomized turning points is also realized and the dynamical behavior has been investigated.Comment: 20 pages 12 figures, 1 table, to appear in Comp. Phys. Com

Computational modelling of diffusion magnetic resonance imaging based on cardiac histology

The exact relationship between changes in myocardial microstructure as a result of heart disease and the signal measured using diffusion tensor cardiovascular magnetic resonance (DT-CMR) is currently not well understood. Computational modelling of diffusion in combination with realistic numerical phantoms offers the unique opportunity to study effects of pathologies or the efficacy of improvements to acquisition protocols in a controlled in-silico environment. In this work, Monte Carlo random walk (MCRW) methods are used to simulate diffusion in a histology-based 3D model of the myocardium. Sensitivity of typical DT-CMR sequences to changes in tissue properties is assessed. First, myocardial tissue is analysed to identify important geometric features and diffusion parameters. A two-compartment model is considered where intra-cellular compartments with a reduced bulk diffusion coefficient are separated from extra-cellular space by permeable membranes. Secondary structures like groups of cardiomyocyte (sheetlets) must also be included, and different methods are developed to automatically generate realistic histology-based substrates. Next, in-silico simulation of DT-CMR is reviewed and a tool to generate idealised versions of common pulse sequences is discussed. An efficient GPU-based numerical scheme for obtaining a continuum solution to the Bloch--Torrey equations is presented and applied to domains directly extracted from histology images. In order to verify the numerical methods used throughout this work, an analytical solution to the diffusion equation in 1D is described. It relies on spectral analysis of the diffusion operator and requires that all roots of a complex transcendental equation are found. To facilitate a fast and reliable solution, a novel root finding algorithm based on Chebyshev polynomial interpolation is proposed. To simulate realistic 3D geometries MCRW methods are employed. A parallel simulator for both grid-based and surface mesh--based geometries is presented. The presence of permeable membranes requires special treatment. For this, a commonly used transit model is analysed. Finally, the methods above are applied to study the effect of various model and sequence parameters on DT-CMR results. Simulations with impermeable membranes reveal sequence-specific sensitivity to extra-cellular volume fraction and diffusion coefficients. By including membrane permeability, DT-CMR results further approach values expected in vivo.Open Acces

An investigation of the efficient implementation of Cellular Automata on multi-core CPU and GPU hardware

Copyright © 2015 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Parallel and Distributed Computing . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Parallel and Distributed Computing Vol. 77 (2015), DOI: 10.1016/j.jpdc.2014.10.011Cellular automata (CA) have proven to be excellent tools for the simulation of a wide variety of phenomena in the natural world. They are ideal candidates for acceleration with modern general purpose-graphical processing units (GPU/GPGPU) hardware that consists of large numbers of small, tightly-coupled processors. In this study the potential for speeding up CA execution using multi-core CPUs and GPUs is investigated and the scalability of doing so with respect to standard CA parameters such as lattice and neighbourhood sizes, number of states and generations is determined. Additionally the impact of ‘Activity’ (the number of ‘alive’ cells) within a given CA simulation is investigated in terms of both varying the random initial distribution levels of ‘alive’ cells, and via the use of novel state transition rules; where a change in the dynamics of these rules (i.e. the number of states) allows for the investigation of the variable complexity within.Engineering and Physical Sciences Research Council (EPSRC

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware