arXiv subjects

Ray W. Grout

Publications and source records attributed to Ray W. Grout.

4 recordsLinked to original sources

arXiv2019

Deep learning for presumed probability density function models

In this work, we use ML techniques to develop presumed PDF models for large eddy simulations of reacting flows. The joint sub-filter PDF of mixture fraction and progress variable is modeled using various ML algorithms and commonly used analytical models. The ML algorithms evaluated in the work are representative of three major classes of ML techniques: traditional ensemble methods (random forests), deep learning (deep neural networks), and generative learning (variational autoencoders). The first two algorithms are supervised learning algorithms, and the third is an unsupervised learning algorithm. Data from direct numerical simulation of the low-swirl burner (Day et al. 2012) are used to develop training data for sub-filter PDF models. Models are evaluated on predictions of the sub-filter PDFs as well as predictions of the filtered reaction rate of the progress variable, computed through a convolution of the sub-filter PDF and the conditional means of the reaction rate. This a-priori modeling study demonstrates that deep learning models for presumed PDF modeling are three times more accurate than analytical beta-beta PDF models. These models are as accurate as random forest models while using five times fewer trainable parameters and being 25 times faster for inference. We illustrate how models generalize to other regions of the flow and develop criteria based on the Jensen-Shannon divergence to quantify the performance of a model on new data.

physics.comp-ph↗

arXiv2019

A block-random algorithm for learning on distributed, heterogeneous data

Most deep learning models are based on deep neural networks with multiple layers between input and output. The parameters defining these layers are initialized using random values and are "learned" from data, typically using stochastic gradient descent based algorithms. These algorithms rely on data being randomly shuffled before optimization. The randomization of the data prior to processing in batches that is formally required for stochastic gradient descent algorithm to effectively derive a useful deep learning model is expected to be prohibitively expensive for in situ model training because of the resulting data communications across the processor nodes. We show that the stochastic gradient descent (SGD) algorithm can still make useful progress if the batches are defined on a per-processor basis and processed in random order even though (i) the batches are constructed from data samples from a single class or specific flow region, and (ii) the overall data samples are heterogeneous. We present block-random gradient descent, a new algorithm that works on distributed, heterogeneous data without having to pre-shuffle. This algorithm enables in situ learning for exascale simulations. The performance of this algorithm is demonstrated on a set of benchmark classification models and the construction of a subgrid scale large eddy simulations (LES) model for turbulent channel flow using a data model similar to that which will be encountered in exascale simulation.

cs.LG↗

arXiv2019

Data recovery in computational fluid dynamics through deep image priors

One of the challenges encountered by computational simulations at exascale is the reliability of simulations in the face of hardware and software faults. These faults, expected to increase with the complexity of the computational systems, will lead to the loss of simulation data and simulation failure and are currently addressed through a checkpoint-restart paradigm. Focusing specifically on computational fluid dynamics simulations, this work proposes a method that uses a deep convolutional neural network to recover simulation data. This data recovery method (i) is agnostic to the flow configuration and geometry, (ii) does not require extensive training data, and (iii) is accurate for very different physical flows. Results indicate that the use of deep image priors for data recovery is more accurate than standard recovery techniques, such as the Gaussian process regression, also known as Kriging. Data recovery is performed for two canonical fluid flows: laminar flow around a cylinder and homogeneous isotropic turbulence. For data recovery of the laminar flow around a cylinder, results indicate similar performance between the proposed method and Gaussian process regression across a wide range of mask sizes. For homogeneous isotropic turbulence, data recovery through the deep convolutional neural network exhibits an error in relevant turbulent quantities approximately three times smaller than that for the Gaussian process regression,. Forward simulations using recovered data illustrate that the enstrophy decay is captured within 10% using the deep convolutional neural network approach. Although demonstrated specifically for data recovery of fluid flows, this technique can be used in a wide range of applications, including particle image velocimetry, visualization, and computational simulations of physical processes beyond the Navier-Stokes equations.

physics.flu-dyn↗

arXiv2016

Iterative importance sampling algorithms for parameter estimation

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicability of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using "coarse" MCMC runs or Gaussian mixture models.

math.NA↗