35,348 research outputs found
Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems
This paper deals with the definition and optimization of augmentation spaces
for faster convergence of the conjugate gradient method in the resolution of
sequences of linear systems. Using advanced convergence results from the
literature, we present a procedure based on a selection of relevant
approximations of the eigenspaces for extracting, selecting and reusing
information from the Krylov subspaces generated by previous solutions in order
to accelerate the current iteration. Assessments of the method are proposed in
the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24
page
Improvements to deep convolutional neural networks for LVCSR
Deep Convolutional Neural Networks (CNNs) are more powerful than Deep Neural
Networks (DNN), as they are able to better reduce spectral variation in the
input signal. This has also been confirmed experimentally, with CNNs showing
improvements in word error rate (WER) between 4-12% relative compared to DNNs
across a variety of LVCSR tasks. In this paper, we describe different methods
to further improve CNN performance. First, we conduct a deep analysis comparing
limited weight sharing and full weight sharing with state-of-the-art features.
Second, we apply various pooling strategies that have shown improvements in
computer vision to an LVCSR speech task. Third, we introduce a method to
effectively incorporate speaker adaptation, namely fMLLR, into log-mel
features. Fourth, we introduce an effective strategy to use dropout during
Hessian-free sequence training. We find that with these improvements,
particularly with fMLLR and dropout, we are able to achieve an additional 2-3%
relative improvement in WER on a 50-hour Broadcast News task over our previous
best CNN baseline. On a larger 400-hour BN task, we find an additional 4-5%
relative improvement over our previous best CNN baseline.Comment: 6 pages, 1 figur
Minimizing synchronizations in sparse iterative solvers for distributed supercomputers
Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrates how to minimizing global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and is verified by numerical experiments using up to 900 processors. The experiments also show the communication complexity for some structured sparse matrix vector multiplications and global communications in the underlying supercomputers are in the order P1/2.5 and P4/5 respectively, where P is the number of processors and the experiments were carried on a Dawning 5000A
Inner product computation for sparse iterative solvers on\ud distributed supercomputer
Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale
Second order adjoints for solving PDE-constrained optimization problems
Inverse problems are of utmost importance in many fields of science and engineering. In the
variational approach inverse problems are formulated as PDE-constrained optimization problems,
where the optimal estimate of the uncertain parameters is the minimizer of a certain cost
functional subject to the constraints posed by the model equations. The numerical solution
of such optimization problems requires the computation of derivatives of the model output
with respect to model parameters. The first order derivatives of a cost functional (defined
on the model output) with respect to a large number of model parameters can be calculated
efficiently through first order adjoint sensitivity analysis. Second order adjoint models
give second derivative information in the form of matrix-vector products between the Hessian
of the cost functional and user defined vectors. Traditionally, the construction of second
order derivatives for large scale models has been considered too costly. Consequently, data
assimilation applications employ optimization algorithms that use only first order derivative
information, like nonlinear conjugate gradients and quasi-Newton methods.
In this paper we discuss the mathematical foundations of second order adjoint sensitivity
analysis and show that it provides an efficient approach to obtain Hessian-vector products. We
study the benefits of using of second order information in the numerical optimization process
for data assimilation applications. The numerical studies are performed in a twin experiment
setting with a two-dimensional shallow water model. Different scenarios are considered with
different discretization approaches, observation sets, and noise levels. Optimization algorithms
that employ second order derivatives are tested against widely used methods that require
only first order derivatives. Conclusions are drawn regarding the potential benefits and the
limitations of using high-order information in large scale data assimilation problems
The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2
Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution
Towards Lattice Quantum Chromodynamics on FPGA devices
In this paper we describe a single-node, double precision Field Programmable
Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the
context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we
invert numerically the Dirac-Wilson operator on a 4-dimensional grid on three
Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250
accelerator and the largest device available on the market, the VU13P device.
In our implementation we separate software/hardware parts in such a way that
the entire multiplication by the Dirac operator is performed in hardware, and
the rest of the algorithm runs on the host. We find out that the FPGA
implementation can offer a performance comparable with that obtained using
current CPU or Intel's many core Xeon Phi accelerators. A possible multiple
node FPGA-based system is discussed and we argue that power-efficient High
Performance Computing (HPC) systems can be implemented using FPGA devices only.Comment: 17 pages, 4 figure
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