Ray W. Grout

Matthias Morzfeld, Marcus S. Day, Ray W. Grout et al.

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.

Prakash Mohan, Marc T. Henry de Frahan, Ryan King et al.

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.