555 research outputs found
Spherical harmonic transform with GPUs
We describe an algorithm for computing an inverse spherical harmonic
transform suitable for graphic processing units (GPU). We use CUDA and base our
implementation on a Fortran90 routine included in a publicly available parallel
package, S2HAT. We focus our attention on the two major sequential steps
involved in the transforms computation, retaining the efficient parallel
framework of the original code. We detail optimization techniques used to
enhance the performance of the CUDA-based code and contrast them with those
implemented in the Fortran90 version. We also present performance comparisons
of a single CPU plus GPU unit with the S2HAT code running on either a single or
4 processors. In particular we find that use of the latest generation of GPUs,
such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms
by as much as 18 times with respect to S2HAT executed on one core, and by as
much as 5.5 with respect to S2HAT on 4 cores, with the overall performance
being limited by the Fast Fourier transforms. The work presented here has been
performed in the context of the Cosmic Microwave Background simulations and
analysis. However, we expect that the developed software will be of more
general interest and applicability
Parallel Spherical Harmonic Transforms on heterogeneous architectures (GPUs/multi-core CPUs)
Spherical Harmonic Transforms (SHT) are at the heart of many scientific and
practical applications ranging from climate modelling to cosmological
observations. In many of these areas new, cutting-edge science goals have been
recently proposed requiring simulations and analyses of experimental or
observational data at very high resolutions and of unprecedented volumes. Both
these aspects pose formidable challenge for the currently existing
implementations of the transforms.
This paper describes parallel algorithms for computing SHT with two variants
of intra-node parallelism appropriate for novel supercomputer architectures,
multi-core processors and Graphic Processing Units (GPU). It also discusses
their performance, alone and embedded within a top-level, MPI-based
parallelisation layer ported from the S2HAT library, in terms of their
accuracy, overall efficiency and scalability. We show that our inverse SHT run
on GeForce 400 Series GPUs equipped with latest CUDA architecture ("Fermi")
outperforms the state of the art implementation for a multi-core processor
executed on a current Intel Core i7-2600K. Furthermore, we show that an
MPI/CUDA version of the inverse transform run on a cluster of 128 Nvidia Tesla
S1070 is as much as 3 times faster than the hybrid MPI/OpenMP version executed
on the same number of quad-core processors Intel Nahalem for problem sizes
motivated by our target applications. Performance of the direct transforms is
however found to be at the best comparable in these cases. We discuss in detail
the algorithmic solutions devised for major steps involved in the transforms
calculation, emphasising those with a major impact on their overall
performance, and elucidates the sources of the dichotomy between the direct and
the inverse operations
A GPU-accelerated Direct-sum Boundary Integral Poisson-Boltzmann Solver
In this paper, we present a GPU-accelerated direct-sum boundary integral
method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a
well-posed boundary integral formulation is used to ensure the fast convergence
of Krylov subspace based linear algebraic solver such as the GMRES. The
molecular surfaces are discretized with flat triangles and centroid
collocation. To speed up our method, we take advantage of the parallel nature
of the boundary integral formulation and parallelize the schemes within CUDA
shared memory architecture on GPU. The schemes use only
size-of-double device memory for a biomolecule with triangular surface
elements and partial charges. Numerical tests of these schemes show
well-maintained accuracy and fast convergence. The GPU implementation using one
GPU card (Nvidia Tesla M2070) achieves 120-150X speed-up to the implementation
using one CPU (Intel L5640 2.27GHz). With our approach, solving PB equations on
well-discretized molecular surfaces with up to 300,000 boundary elements will
take less than about 10 minutes, hence our approach is particularly suitable
for fast electrostatics computations on small to medium biomolecules
Acceleration Techniques for Sparse Recovery Based Plane-wave Decomposition of a Sound Field
Plane-wave decomposition by sparse recovery is a reliable and accurate technique for plane-wave decomposition which can be used for source localization, beamforming, etc. In this work, we introduce techniques to accelerate the plane-wave decomposition by sparse recovery. The method consists of two main algorithms which are spherical Fourier transformation (SFT) and sparse recovery. Comparing the two algorithms, the sparse recovery is the most computationally intensive. We implement the SFT on an FPGA and the sparse recovery on a multithreaded computing platform. Then the multithreaded computing platform could be fully utilized for the sparse recovery. On the other hand, implementing the SFT on an FPGA helps to flexibly integrate the microphones and improve the portability of the microphone array. For implementing the SFT on an FPGA, we develop a scalable FPGA design model that enables the quick design of the SFT architecture on FPGAs. The model considers the number of microphones, the number of SFT channels and the cost of the FPGA and provides the design of a resource optimized and cost-effective FPGA architecture as the output. Then we investigate the performance of the sparse recovery algorithm executed on various multithreaded computing platforms (i.e., chip-multiprocessor, multiprocessor, GPU, manycore). Finally, we investigate the influence of modifying the dictionary size on the computational performance and the accuracy of the sparse recovery algorithms. We introduce novel sparse-recovery techniques which use non-uniform dictionaries to improve the performance of the sparse recovery on a parallel architecture
Multi-Architecture Monte-Carlo (MC) Simulation of Soft Coarse-Grained Polymeric Materials: SOft coarse grained Monte-carlo Acceleration (SOMA)
Multi-component polymer systems are important for the development of new
materials because of their ability to phase-separate or self-assemble into
nano-structures. The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction
with a soft, coarse-grained polymer model is an established technique to
investigate these soft-matter systems. Here we present an im- plementation of
this method: SOft coarse grained Monte-carlo Accelera- tion (SOMA). It is
suitable to simulate large system sizes with up to billions of particles, yet
versatile enough to study properties of different kinds of molecular
architectures and interactions. We achieve efficiency of the simulations
commissioning accelerators like GPUs on both workstations as well as
supercomputers. The implementa- tion remains flexible and maintainable because
of the implementation of the scientific programming language enhanced by
OpenACC pragmas for the accelerators. We present implementation details and
features of the program package, investigate the scalability of our
implementation SOMA, and discuss two applications, which cover system sizes
that are difficult to reach with other, common particle-based simulation
methods
A Geometric Deep Learning Approach to Sound Source Localization and Tracking
La localización y el tracking de fuentes sonoras mediante agrupaciones de micrófonos es un problema que, pese a llevar décadas siendo estudiado, permanece abierto. En los últimos años, modelos basados en deep learning han superado el estado del arte que habÃa sido establecido por las técnicas clásicas de procesado de señal, pero estos modelos todavÃa presentan problemas para trabajar en espacios con alta reverberación o para realizar el tracking de varias fuentes sonoras, especialmente cuando no es posible aplicar ningún criterio para clasificarlas u ordenarlas. En esta tesis, se proponen nuevos modelos que, basados en las ideas del Geometric Deep Learning, suponen un avance en el estado del arte para las situaciones mencionadas previamente.Los modelos propuestos utilizan como entrada mapas de potencia acústica calculados con el algoritmo SRP-PHAT, una técnica clásica de procesado de señal que permite estimar la energÃa acústica recibida desde cualquier dirección del espacio. Además, también proponemos una nueva técnica para suprimir analÃticamente el efecto de una fuente en las funciones de correlación cruzada usadas para calcular los mapas SRP-PHAT. Basándonos en técnicas de banda estrecha, se demuestra que es posible proyectar las funciones de correlación cruzada de las señales capturadas por una agrupación de micrófonos a un espacio ortogonal a una dirección dada simplemente usando una combinación lineal de las funciones originales con retardos temporales. La técnica propuesta puede usarse para diseñar sistemas iterativos de localización de múltiples fuentes que, tras localizar la fuente con mayor energÃa en las funciones de correlación cruzada o en los mapas SRP-PHAT, la cancelen para poder encontrar otras fuentes que estuvieran enmascaradas por ella.Antes de poder entrenar modelos de deep learning necesitamos datos. Esto, en el caso de seguir un esquema de aprendizaje supervisado, supone un dataset de grabaciones de audio multicanal con la posición de las fuentes etiquetada con precisión. Pese a que existen algunos datasets con estas caracterÃsticas, estos no son lo suficientemente extensos para entrenar una red neuronal y los entornos acústicos que incluyen no son suficientemente variados. Para solventar el problema de la falta de datos, presentamos una técnica para simular escenas acústicas con una o varias fuentes en movimiento y, para realizar estas simulaciones conforme son necesarias durante el entrenamiento de la red, presentamos la que es, que sepamos, la primera librerÃa de software libre para la simulación de acústica de salas con aceleración por GPU. Tal y como queda demostrado en esta tesis, esta librerÃa es más de dos órdenes de magnitud más rápida que otras librerÃas del estado del arte.La idea principal del Geometric Deep Learning es que los modelos deberÃan compartir las simetrÃas (i.e. las invarianzas y equivarianzas) de los datos y el problema que se quiere resolver. Para la estimación de la dirección de llegada de una única fuente, el uso de mapas SRP-PHAT como entrada de nuestros modelos hace que la equivarianza a las rotaciones sea obvia y, tras presentar una primera aproximación usando redes convolucionales tridimensionales, presentamos un modelo basado en convoluciones icosaédricas que son capaces de aproximar la equivarianza al grupo continuo de rotaciones esféricas por la equivarianza al grupo discreto de las 60 simetrÃas del icosaedro. En la tesis se demuestra que los mapas SRP-PHAT son una caracterÃstica de entrada mucho más robusta que los espectrogramas que se usan tÃpicamente en muchos modelos del estado del arte y que el uso de las convoluciones icosaédricas, combinado con una nueva función softargmax que obtiene una salida de regresión a partir del resultado de una red convolucional interpretándolo como una distribución de probabilidad y calculando su valor esperado, permite reducir enormemente el número de parámetros entrenables de los modelos sin reducir la precisión de sus estimaciones.Cuando queremos realizar el tracking de varias fuentes en movimiento y no podemos aplicar ningún criterio para ordenarlas o clasificarlas, el problema se vuelve invariante a las permutaciones de las estimaciones, por lo que no podemos compararlas directamente con las etiquetas de referencia dado que no podemos esperar que sigan el mismo orden. Este tipo de modelos se han entrenado tÃpicamente usando estrategias de entrenamiento invariantes a las permutaciones, pero estas normalmente no penalizan los cambios de identidad por lo que los modelos entrenados con ellas no mantienen la identidad de cada fuente de forma consistente. Para resolver este problema, en esta tesis proponemos una nueva estrategia de entrenamiento, a la que llamamos sliding permutation invariant training (sPIT), que es capaz de optimizar todas las caracterÃsticas que podemos esperar de un sistema de tracking de múltiples fuentes: la precisión de sus estimaciones de dirección de llegada, la exactitud de sus detecciones y la consistencia de las identidades asignadas a cada fuente.Finalmente, proponemos un nuevo tipo de red recursiva que usa conjuntos de vectores en lugar de vectores para representar su entrada y su estado y que es invariante a las permutaciones de los elementos del conjunto de entrada y equivariante a las del conjunto de estado. En esta tesis se muestra como este es el comportamiento que deberÃamos esperar de un sistema de tracking que toma como entradas las estimaciones de un modelo de localización multifuente y se compara el rendimiento de estas redes recursivas invariantes a las permutaciones con redes recursivas GRU convencionales para aplicaciones de tracking de fuentes sonoras.The localization and tracking of sound sources using microphone arrays is a problem that, even if it has attracted attention from the signal processing research community for decades, remains open. In recent years, deep learning models have surpassed the state-of-the-art that had been established by classic signal processing techniques, but these models still struggle with handling rooms with strong reverberations or tracking multiple sources that dynamically appear and disappear, especially when we cannot apply any criteria to classify or order them. In this thesis, we follow the ideas of the Geometric Deep Learning framework to propose new models and techniques that mean an advance of the state-of-the-art in the aforementioned scenarios. As the input of our models, we use acoustic power maps computed using the SRP-PHAT algorithm, a classic signal processing technique that allows us to estimate the acoustic energy received from any direction of the space and, therefore, compute arbitrary-shaped power maps. In addition, we also propose a new technique to analytically cancel a source from the generalized cross-correlations used to compute the SRP-PHAT maps. Based on previous narrowband cancellation techniques, we prove that we can project the cross-correlation functions of the signals captured by a microphone array into a space orthogonal to a given direction by just computing a linear combination of time-shifted versions of the original cross-correlations. The proposed cancellation technique can be used to design iterative multi-source localization systems where, after having found the strongest source in the generalized cross-correlation functions or in the SRP-PHAT maps, we can cancel it and find new sources that were previously masked by thefirst source. Before being able to train deep learning models we need data, which, in the case of following a supervised learning approach, means a dataset of multichannel recordings with the position of the sources accurately labeled. Although there exist some datasets like this, they are not large enough to train a neural network and the acoustic environments they include are not diverse enough. To overcome this lack of real data, we present a technique to simulate acoustic scenes with one or several moving sound sources and, to be able to perform these simulations as they are needed during the training, we present what is, to the best of our knowledge, the first free and open source room acoustics simulation library with GPU acceleration. As we prove in this thesis, the presented library is more than two orders of magnitude faster than other state-of-the-art CPU libraries. The main idea of the Geometric Deep Learning philosophy is that the models should fit the symmetries (i.e. the invariances and equivariances) of the data and the problem we want to solve. For single-source direction of arrival estimation, the use of SRP-PHAT maps as inputs of our models makes the rotational equivariance of the problem undeniably clear and, after a first approach using 3D convolutional neural networks, we present a model using icosahedral convolutions that approximate the equivariance to the continuous group of spherical rotations by the discrete group of the 60 icosahedral symmetries. We prove that the SRP-PHAT maps are a much more robust input feature than the spectrograms typically used in many state-of-the-art models and that the use of the icosahedral convolutions, combined with a new soft-argmax function that obtains a regression output from the output of the convolutional neural network by interpreting it as a probability distribution and computing its expected value, allows us to dramatically reduce the number of trainable parameters of the models without losing accuracy in their estimations. When we want to track multiple moving sources and we cannot use any criteria to order or classify them, the problem becomes invariant to the permutations of the estimates, so we cannot directly compare them with the ground truth labels since we cannot expect them to be in the same order. This kind of models has typically been trained using permutation invariant training strategies, but these strategies usually do not penalize the identity switches and the models trained with them do not keep the identity of every source consistent during the tracking. To solve this issue, we propose a new training strategy, which we call sliding permutation invariant training, that is able to optimize all the features that we could expect from a multi-source tracking system: the precision of the direction of arrival estimates, the accuracy of the source detections, and the consistency of the assigned identities. Finally, we propose a new kind of recursive neural network that, instead of using vectors as their input and their state, uses sets of vectors and is invariant to the permutation of the elements of the input set and equivariant to the permutations of the elements of the state set. We show how this is the behavior that we should expect from a tracking model which takes as inputs the estimates of a multi-source localization model and compare these permutation-invariant recursive neural networks with the conventional gated recurrent units for sound source tracking applications.<br /
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