GPUs

Data-driven fluid flow modeling

Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reductionJ. Hampton, HR. Fairbanks, A. Narayan, A. Doostan. In Journal of Computational Physics, Vol. 368, Elsevier BV, pp. 315--332. September, 2018. DOI: 10.1016/j.jcp.2018.04.015 For practical model-based demands, such as design space exploration and uncertainty quantification (UQ), a high-fidelity model that produces accurate outputs often has high computational cost, while a low-fidelity model with less accurate outputs has low computational cost. It is often possible to construct a bi-fidelity model having accuracy comparable with the high-fidelity model and computational cost comparable with the low-fidelity model. This work presents the construction and analysis of a non-intrusive (i.e., sample-based) bi-fidelity model that relies on the low-rank structure of the map between model parameters/uncertain inputs and the solution of interest, if exists. Specifically, we derive a novel, pragmatic estimate for the error committed by this bi-fidelity model. We show that this error bound can be used to determine if a given pair of low- and high-fidelity models will lead to an accurate bi-fidelity approximation. The cost of this error bound is relatively small and depends on the solution rank. The value of this error estimate is demonstrated using two example problems in the context of UQ, involving linear and non-linear partial differential equations. |

Fast predictive models based on multi-fidelity sampling of properties in molecular dynamics simulationsM. Razi, A. Narayan, RM. Kirby, D. Bedrov. In Computational Materials Science, Vol. 152, Elsevier BV, pp. 125--133. September, 2018. DOI: 10.1016/j.commatsci.2018.05.029 In this paper we introduce a novel approach for enhancing the sampling convergence for properties predicted by molecular dynamics. The proposed approach is based upon the construction of a multi-fidelity surrogate model using computational models with different levels of accuracy. While low fidelity models produce result with a lower level of accuracy and computational cost, in this framework they can provide the basis for identification of the optimal sparse sampling pattern for high fidelity models to construct an accurate surrogate model. Such an approach can provide a significant computational saving for the estimation of the quantities of interest for the underlying physical/engineering systems. In the present work, this methodology is demonstrated for molecular dynamics simulations of a Lennard-Jones fluid. Levels of multi-fidelity are defined based upon the integration time step employed in the simulation. The proposed approach is applied to two different canonical problems including (i) single component fluid and (ii) binary glass-forming mixture. The results show about 70% computational saving for the estimation of averaged properties of the systems such as total energy, self diffusion coefficient, radial distribution function and mean squared displacements with a reasonable accuracy. |

Scalable Data Management of the Uintah Simulation Framework for Next-Generation Engineering Problems with RadiationS. Kumar, A. Humphrey, W. Usher, S. Petruzza, B. Peterson, J. A. Schmidt, D. Harris, B. Isaac, J. Thornock, T. Harman, V. Pascucci,, M. Berzins. In Supercomputing Frontiers, Springer International Publishing, pp. 219--240. 2018. ISBN: 978-3-319-69953-0 DOI: 10.1007/978-3-319-69953-0_13 The need to scale next-generation industrial engineering problems to the largest computational platforms presents unique challenges. This paper focuses on data management related problems faced by the Uintah simulation framework at a production scale of 260K processes. Uintah provides a highly scalable asynchronous many-task runtime system, which in this work is used for the modeling of a 1000 megawatt electric (MWe) ultra-supercritical (USC) coal boiler. At 260K processes, we faced both parallel I/O and visualization related challenges, e.g., the default file-per-process I/O approach of Uintah did not scale on Mira. In this paper we present a simple to implement, restructuring based parallel I/O technique. We impose a restructuring step that alters the distribution of data among processes. The goal is to distribute the dataset such that each process holds a larger chunk of data, which is then written to a file independently. This approach finds a middle ground between two of the most common parallel I/O schemes--file per process I/O and shared file I/O--in terms of both the total number of generated files, and the extent of communication involved during the data aggregation phase. To address scalability issues when visualizing the simulation data, we developed a lightweight renderer using OSPRay, which allows scientists to visualize the data interactively at high quality and make production movies. Finally, this work presents a highly efficient and scalable radiation model based on the sweeping method, which significantly outperforms previous approaches in Uintah, like discrete ordinates. The integrated approach allowed the USC boiler problem to run on 260K CPU cores on Mira. |

Nonlinear stability and time step selection for the MPM methodM. Berzins. In Computational Particle Mechanics, Jan, 2018. ISSN: 2196-4386 DOI: 10.1007/s40571-018-0182-y The Material Point Method (MPM) has been developed from the Particle in Cell (PIC) method over the last 25 years and has proved its worth in solving many challenging problems involving large deformations. Nevertheless there are many open questions regarding the theoretical properties of MPM. For example in while Fourier methods, as applied to PIC may provide useful insight, the non-linear nature of MPM makes it necessary to use a full non-linear stability analysis to determine a stable time step for MPM. In order to begin to address this the stability analysis of Spigler and Vianello is adapted to MPM and used to derive a stable time step bound for a model problem. This bound is contrasted against traditional Speed of sound and CFL bounds and shown to be a realistic stability bound for a model problem. |

Research and Education in Computational Science and EngineeringU. Ruede, K. Willcox, L. C. McInnes, H. De Sterck, G. Biros, H. Bungartz, J. Corones, E. Cramer, J. Crowley, O. Ghattas, M. Gunzburger, M. Hanke, R. Harrison, M. Heroux, J. Hesthaven, P. Jimack, C. Johnson, K. E. Jordan, D. E. Keyes, R. Krause, V. Kumar, S. Mayer, J. Meza, K. M. Mrken, J. T. Oden, L. Petzold, P. Raghavan, S. M. Shontz, A. Trefethen, P. Turner, V. Voevodin, B. Wohlmuth,, C. S. Woodward. In SIAM Review, Vol. 60, No. 3, SIAM, pp. 707--754. Jan, 2018. DOI: 10.1137/16m1096840 This report presents challenges, opportunities and directions for computational science and engineering (CSE) research and education for the next decade. Over the past two decades the field of CSE has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers with algorithmic inventions and software systems that transcend disciplines and scales. CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments—including the architectural complexity of extreme-scale computing, the data revolution and increased attention to data-driven discovery, and the specialization required to follow the applications to new frontiers—is redefining the scope and reach of the CSE endeavor. With these many current and expanding opportunities for the CSE field, there is a growing demand for CSE graduates and a need to expand CSE educational offerings. This need includes CSE programs at both the undergraduate and graduate levels, as well as continuing education and professional development programs, exploiting the synergy between computational science and data science. Yet, as institutions consider new and evolving educational programs, it is essential to consider the broader research challenges and opportunities that provide the context for CSE education and workforce development. |

ISAVS: Interactive Scalable Analysis and Visualization SystemS. Petruzza, A. Venkat, A. Gyulassy, G. Scorzelli, F. Federer, A. Angelucci, V. Pascucci, P. T. Bremer. In ACM SIGGRAPH Asia 2017 Symposium on Visualization, ACM Press, 2017. DOI: 10.1145/3139295.3139299 Modern science is inundated with ever increasing data sizes as computational capabilities and image acquisition techniques continue to improve. For example, simulations are tackling ever larger domains with higher fidelity, and high-throughput microscopy techniques generate larger data that are fundamental to gather biologically and medically relevant insights. As the image sizes exceed memory, and even sometimes local disk space, each step in a scientific workflow is impacted. Current software solutions enable data exploration with limited interactivity for visualization and analytic tasks. Furthermore analysis on HPC systems often require complex hand-written parallel implementations of algorithms that suffer from poor portability and maintainability. We present a software infrastructure that simplifies end-to-end visualization and analysis of massive data. First, a hierarchical streaming data access layer enables interactive exploration of remote data, with fast data fetching to test analytics on subsets of the data. Second, a library simplifies the process of developing new analytics algorithms, allowing users to rapidly prototype new approaches and deploy them in an HPC setting. Third, a scalable runtime system automates mapping analysis algorithms to whatever computational hardware is available, reducing the complexity of developing scaling algorithms. We demonstrate the usability and performance of our system using a use case from neuroscience: filtering, registration, and visualization of tera-scale microscopy data. We evaluate the performance of our system using a leadership-class supercomputer, Shaheen II. |

Multi-Dimensional Filtering: Reducing the Dimension Through Rotation Read More: https://epubs.siam.org/doi/abs/10.1137/16M1097845J. Docampo-Sánchez, J.K. Ryan, M. Mirzargar, R.M. Kirby. In SIAM Journal on Scientific Computing, Vol. 39, No. 5, SIAM, pp. A2179--A2200. Jan, 2017. DOI: 10.1137/16m1097845 Over the past few decades there has been a strong effort toward the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this postprocessor. These advantages can be exploited during flow visualization, for example, by applying the SIAC filter to DG data before streamline computations [M. Steffen, S. Curtis, R. M. Kirby, and J. K. Ryan, IEEE Trans. Vis. Comput. Graphics, 14 (2008), pp. 680--692]. However, introducing these filters in engineering applications can be challenging since a tensor product filter grows in support size as the field dimension increases, becoming computationally expensive. As an alternative, [D. Walfisch, J. K. Ryan, R. M. Kirby, and R. Haimes, J. Sci. Comput., 38 (2009), pp. 164--184] proposed a univariate filter implemented along the streamline curves. Until now, this technique remained a numerical experiment. In this paper we introduce the line SIAC filter and explore how the orientation, structure, and filter size affect the order of accuracy and global errors. We present theoretical error estimates showing how line filtering preserves the properties of traditional tensor product filtering, including smoothness and improvement in the convergence rate. Furthermore, numerical experiments are included, exhibiting how these filters achieve the same accuracy at significantly lower computational costs, becoming an attractive tool for the scientific visualization community. |

Hexagonal Smoothness-Increasing Accuracy-Conserving FilteringM. Mirzargar, A. Jallepalli, J.K. Ryan, R.M. Kirby. In Journal of Scientific Computing, Vol. 73, No. 2-3, Springer Nature, pp. 1072--1093. Aug, 2017. DOI: 10.1007/s10915-017-0517-5 Discontinuous Galerkin (DG) methods are a popular class of numerical techniques to solve partial differential equations due to their higher order of accuracy. However, the inter-element discontinuity of a DG solution hinders its utility in various applications, including visualization and feature extraction. This shortcoming can be alleviated by postprocessing of DG solutions to increase the inter-element smoothness. A class of postprocessing techniques proposed to increase the inter-element smoothness is SIAC filtering. In addition to increasing the inter-element continuity, SIAC filtering also raises the convergence rate from order k+1 to order 2k+1. Since the introduction of SIAC filtering for univariate hyperbolic equations by Cockburn et al. (Math Comput 72(242):577–606, 2003), many generalizations of SIAC filtering have been proposed. Recently, the idea of dimensionality reduction through rotation has been the focus of studies in which a univariate SIAC kernel has been used to postprocess a two-dimensional DG solution (Docampo-Sánchez et al. in Multi-dimensional filtering: reducing the dimension through rotation, 2016. arXiv preprint arXiv:1610.02317). However, the scope of theoretical development of multidimensional SIAC filters has never gone beyond the usage of tensor product multidimensional B-splines or the reduction of the filter dimension. In this paper, we define a new SIAC filter called hexagonal SIAC (HSIAC) that uses a nonseparable class of two-dimensional spline functions called hex splines. In addition to relaxing the separability assumption, the proposed HSIAC filter provides more symmetry to its tensor-product counterpart. We prove that the superconvergence property holds for a specific class of structured triangular meshes using HSIAC filtering and provide numerical results to demonstrate and validate our theoretical results. |

Offline-Enhanced Reduced Basis Method Through Adaptive Construction of the Surrogate Training SetJ. Jiang, Y. Chen, A. Narayan. In Journal of Scientific Computing, Vol. 73, No. 2-3, Springer Nature, pp. 853--875. September, 2017. DOI: 10.1007/s10915-017-0551-3 The reduced basis method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the offline portion of the algorithm is a greedy algorithm, requiring maximization of an error estimate over parameter space. In practice this maximization is usually performed by replacing the parameter domain continuum with a discrete "training" set. When the dimension of parameter space is large, it is necessary to significantly increase the size of this training set in order to effectively search parameter space. Large training sets diminish the attractiveness of RBM algorithms since this proportionally increases the cost of the offline phase. In this work we propose novel strategies for offline RBM algorithms that mitigate the computational difficulty of maximizing error estimates over a training set. The main idea is to identify a subset of the training set, a "surrogate training set" (STS), on which to perform greedy algorithms. The STS we construct is much smaller in size than the full training set, yet our examples suggest that it is accurate enough to induce the solution manifold of interest at the current offline RBM iteration. We propose two algorithms to construct the STS: our first algorithm, the successive maximization method, is inspired by inverse transform sampling for non-standard univariate probability distributions. The second constructs an STS by identifying pivots in the Cholesky decomposition of an approximate error correlation matrix. We demonstrate the algorithm through numerical experiments, showing that it is capable of accelerating offline RBM procedures without degrading accuracy, assuming that the solution manifold has rapidly decaying Kolmogorov width. |

Reducing network congestion and synchronization overhead during aggregation of hierarchical data,S. Kumar, D. Hoang, S. Petruzza, J. Edwards, V. Pascucci. In 2017 IEEE 24th International Conference on High Performance Computing (HiPC), IEEE, Dec, 2017. DOI: 10.1109/hipc.2017.00034 Hierarchical data representations have been shown to be effective tools for coping with large-scale scientific data. Writing hierarchical data on supercomputers, however, is challenging as it often involves all-to-one communication during aggregation of low-resolution data which tends to span the entire network domain, resulting in several bottlenecks. We introduce the concept of indexing templates, which succinctly describe data organization and can be used to alter movement of data in beneficial ways. We present two techniques, domain partitioning and localized aggregation, that leverage indexing templates to alleviate congestion and synchronization overheads during data aggregation. We report experimental results that show significant I/O speedup using our proposed schemes on two of today's fastest supercomputers, Mira and Shaheen II, using the Uintah and S3D simulation frameworks. |

Reducing Network Congestion and Synchronization Overhead During Aggregation of Hierarchical DataS. Kumar, D. Hoang, S. Petruzza, J. Edwards, V. Pascucci. In 2017 IEEE 24th International Conference on High Performance Computing (HiPC), pp. 223-232. Dec, 2017. DOI: 10.1109/HiPC.2017.00034 Hierarchical data representations have been shown to be effective tools for coping with large-scale scientific data. Writing hierarchical data on supercomputers, however, is challenging as it often involves all-to-one communication during aggregation of low-resolution data which tends to span the entire network domain, resulting in several bottlenecks. We introduce the concept of indexing templates, which succinctly describe data organization and can be used to alter movement of data in beneficial ways. We present two techniques, domain partitioning and localized aggregation, that leverage indexing templates to alleviate congestion and synchronization overheads during data aggregation. We report experimental results that show significant I/O speedup using our proposed schemes on two of today's fastest supercomputers, Mira and Shaheen II, using the Uintah and S3D simulation frameworks. |

Sequential data assimilation with multiple nonlinear models and applications to subsurface flowL. Yang, A. Narayan, P. Wang. In Journal of Computational Physics, Vol. 346, pp. 356--368. Oct, 2017. ISSN: 0021-9991 DOI: 10.1016/j.jcp.2017.06.026 Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes. Meanwhile, available but limited observations of system state could further complicates one's prediction choices. Over the years, data assimilation techniques, such as the Kalman filter, have become essential tools for improved system estimation by incorporating both models forecast and measurement; but its potential to mitigate the impacts of aforementioned model-form uncertainty has yet to be developed. Based on an earlier study of Multi-model Kalman filter, we propose a novel framework to assimilate multiple models with observation data for nonlinear systems, using extended Kalman filter, ensemble Kalman filter and particle filter, respectively. Through numerical examples of subsurface flow, we demonstrate that the new assimilation framework provides an effective and improved forecast of system behaviour. |

A Christoffel function weighted least squares algorithm for collocation approximationsA. Narayan, J. Jakeman, T. Zhou. In Mathematics of Computation, Vol. 86, No. 306, pp. 1913--1947. 2017. ISSN: 0025-5718, 1088-6842 DOI: 10.1090/mcom/3192 We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial Chaos approximation in uncertainty quantification where a polynomial approximation is formed from a combination of orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density of orthogonality. Our proposed algorithm samples with respect to the equilibrium measure of the parametric domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis to motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. |