arXiv subjects

Hans-Joachim Bungartz

Publications and source records attributed to Hans-Joachim Bungartz.

32 records · Page 2Linked to original sources

arXiv2021

preCICE v2: A Sustainable and User-Friendly Coupling Library

preCICE is a free/open-source coupling library. It enables creating partitioned multi-physics simulations by gluing together separate software packages. This paper summarizes the development efforts in preCICE of the past five years. During this time span, we have turned the software from a working prototype -- sophisticated numerical coupling methods and scalability on ten thousands of compute cores -- to a sustainable and user-friendly software project with a steadily-growing community. Today, we know through forum discussions, conferences, workshops, and publications of more than 100 research groups using preCICE. We cover the fundamentals of the software alongside a performance and accuracy analysis of different data mapping methods. Afterwards, we describe ready-to-use integration with widely-used external simulation software packages, tests and continuous integration from unit to system level, and community building measures, drawing an overview of the current preCICE ecosystem.

cs.MS↗

arXiv2021

Model Order Reduction based on Runge-Kutta Neural Network

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems, incorporating Machine Learning to deal with nonlinearity becomes a new choice for reducing complex problems. Such methods usually consist of two steps. The first step is dimension reduction by projection-based method, and the second is the model reconstruction by Neural Network. In this work, we apply some modifications for both steps respectively and investigate how they are impacted by testing with three simulation models. In all cases Proper Orthogonal Decomposition (POD) is used for dimension reduction. For this step, the effects of generating the input snapshot database with constant input parameters is compared with time-dependent input parameters. For the model reconstruction step, two types of neural network architectures are compared: Multilayer Perceptron (MLP) and Runge-Kutta Neural Network (RKNN). The MLP learns the system state directly while RKNN learns the derivative of system state and predicts the new state as a Runge-Kutta integrator.

math.NA↗

arXiv2021

Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve physical effects in an appropriate manner. Since all CFD algorithms scale at least linearly with the size of the underlying mesh discretization, finding an optimal mesh is key for computational efficiency. One methodology used to find optimal meshes is goal-oriented adaptive mesh refinement. However, this is typically computationally demanding and only available in a limited number of tools. Within this contribution, we adopt a machine learning approach to identify optimal mesh densities. We generate optimized meshes using classical methodologies and propose to train a convolutional network predicting optimal mesh densities given arbitrary geometries. The proposed concept is validated along 2d wind tunnel simulations with more than 60,000 simulations. Using a training set of 20,000 simulations we achieve accuracies of more than 98.7%. Corresponding predictions of optimal meshes can be used as input for any mesh generation and CFD tool. Thus without complex computations, any CFD engineer can start his predictions from a high quality mesh.

cs.LG↗

arXiv2020

Fast Approximation of the Gauss-Newton Hessian Matrix for the Multilayer Perceptron

We introduce a fast algorithm for entry-wise evaluation of the Gauss-Newton Hessian (GNH) matrix for the fully-connected feed-forward neural network. The algorithm has a precomputation step and a sampling step. While it generally requires $O(Nn)$ work to compute an entry (and the entire column) in the GNH matrix for a neural network with $N$ parameters and $n$ data points, our fast sampling algorithm reduces the cost to $O(n+d/ε^2)$ work, where $d$ is the output dimension of the network and $ε$ is a prescribed accuracy (independent of $N$). One application of our algorithm is constructing the hierarchical-matrix (H-matrix) approximation of the GNH matrix for solving linear systems and eigenvalue problems. It generally requires $O(N^2)$ memory and $O(N^3)$ work to store and factorize the GNH matrix, respectively. The H-matrix approximation requires only $O(N r_o)$ memory footprint and $O(N r_o^2)$ work to be factorized, where $r_o \ll N$ is the maximum rank of off-diagonal blocks in the GNH matrix. We demonstrate the performance of our fast algorithm and the H-matrix approximation on classification and autoencoder neural networks.

math.NA↗

arXiv2020

Resiliency in Numerical Algorithm Design for Extreme Scale Simulations

This work is based on the seminar titled ``Resiliency in Numerical Algorithm Design for Extreme Scale Simulations'' held March 1-6, 2020 at Schloss Dagstuhl, that was attended by all the authors. Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge.

cs.DC↗

arXiv2020

Quasi-Newton Waveform Iteration for Partitioned Fluid-Structure Interaction

We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multi-rate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation -- a known method to achieve higher order in applications with split time stepping based on continuous representations of coupling variables in time -- with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic test cases -- a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.

math.NA↗

arXiv2019

Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysis

Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse grid approximations are an established approach to overcome these challenges. However, standard adaptivity is based on global information, thus properties such as lower intrinsic stochastic dimensionality or anisotropic coupling of the input directions, which are common in practical applications, are not fully exploited. We propose a novel structure-exploiting dimension-adaptive sparse grid approximation methodology using Sobol' decompositions in each subspace to introduce a sensitivity scoring system to drive the adaptive process. By employing local sensitivity information, we explore and exploit the anisotropic coupling of the stochastic inputs as well as the lower intrinsic stochastic dimensionality. The proposed approach is generic, i.e., it can be formulated in terms of arbitrary approximation operators and point sets. In particular, we consider sparse grid interpolation and pseudo-spectral projection constructed on (L)-Leja sequences. The power and usefulness of the proposed method is demonstrated by applying it to the analysis of gyrokinetic microinstabilities in fusion plasmas, one of the key scientific problems in plasma physics and fusion research. In this context, it is shown that a 12D parameter space can be scanned very efficiently, gaining more than an order of magnitude in computational cost over the standard adaptive approach. Moreover, it allows for the uncertainty propagation and sensitivity analysis in higher-dimensional plasma microturbulence problems, which would be almost impossible to tackle with standard screening approaches.

physics.comp-ph↗

arXiv2019

Multilevel adaptive sparse Leja approximations for Bayesian inverse problems

Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic quadrature is usually unable to efficiently investigate an informative and thus concentrated likelihood. This leads to a large number of required expensive evaluations of the mathematical model. To overcome these challenges, we formulate and test a multilevel adaptive sparse Leja algorithm. At each level, adaptive sparse grid interpolation and quadrature are used to approximate the posterior and perform all quadrature operations, respectively. Specifically, our algorithm uses coarse discretizations of the underlying mathematical model to investigate the parameter space and to identify areas of high posterior probability. Adaptive sparse grid algorithms are then used to place points in these areas, and ignore other areas of small posterior probability. The points are weighted Leja points. As the model discretization is coarse, the construction of the sparse grid is computationally efficient. On this sparse grid, the posterior measure can be approximated accurately with few expensive, fine model discretizations. The efficiency of the algorithm can be enhanced further by exploiting more than two discretization levels. We apply the proposed multilevel adaptive sparse Leja algorithm in numerical experiments involving elliptic inverse problems in 2D and 3D space, in which we compare it with Markov chain Monte Carlo sampling and a standard multilevel approximation.

stat.CO↗

arXiv2018

Computational steering of complex flow simulations

Computational Steering, the combination of a simulation back-end with a visualisation front-end, offers great possibilities to exploit and optimise scenarios in engineering applications. Due to its interactivity, it requires fast grid generation, simulation, and visualisation and, therefore, mostly has to rely on coarse and inaccurate simulations typically performed on rather small interactive computing facilities and not on much more powerful high-performance computing architectures operated in batch-mode. This paper presents a steering environment that intends to bring these two worlds - the interactive and the classical HPC world - together in an integrated way. The environment consists of efficient fluid dynamics simulation codes and a steering and visualisation framework providing a user interface, communication methods for distributed steering, and parallel visualisation tools. The gap between steering and HPC is bridged by a hierarchical approach that performs fast interactive simulations for many scenario variants increasing the accuracy via hierarchical refinements in dependence of the time the user wants to wait. Finally, the user can trigger large simulations for selected setups on an HPC architecture exploiting the pre-computations already done on the interactive system.

cs.CE↗

arXiv2018

Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.

physics.comp-ph↗

arXiv2015

Numerical Model Construction with Closed Observables

Performing analysis, optimization and control using simulations of many-particle systems is computationally demanding when no macroscopic model for the dynamics of the variables of interest is available. In case observations on the macroscopic scale can only be produced via legacy simulator code or live experiments, finding a model for these macroscopic variables is challenging. In this paper, we employ time-lagged embedding theory to construct macroscopic numerical models from output data of a black box, such as a simulator or live experiments. Since the state space variables of the constructed, coarse model are dynamically closed and observable by an observation function, we call these variables closed observables. The approach is an online-offline procedure, as model construction from observation data is performed offline and the new model can then be used in an online phase, independent of the original. We illustrate the theoretical findings with numerical models constructed from time series of a two-dimensional ordinary differential equation system, and from the density evolution of a transport-diffusion system. Applicability is demonstrated in a real-world example, where passengers leave a train and the macroscopic model for the density flow onto the platform is constructed with our approach. If only the macroscopic variables are of interest, simulation runtimes with the numerical model are three orders of magnitude lower compared to simulations with the original fine scale model. We conclude with a brief discussion of possibilities of numerical model construction in systematic upscaling, network optimization and uncertainty quantification.

math.NA↗

arXiv2014

ls1 mardyn: The massively parallel molecular dynamics code for large systems

The molecular dynamics simulation code ls1 mardyn is presented. It is a highly scalable code, optimized for massively parallel execution on supercomputing architectures, and currently holds the world record for the largest molecular simulation with over four trillion particles. It enables the application of pair potentials to length and time scales which were previously out of scope for molecular dynamics simulation. With an efficient dynamic load balancing scheme, it delivers high scalability even for challenging heterogeneous configurations. Presently, multi-center rigid potential models based on Lennard-Jones sites, point charges and higher-order polarities are supported. Due to its modular design, ls1 mardyn can be extended to new physical models, methods, and algorithms, allowing future users to tailor it to suit their respective needs. Possible applications include scenarios with complex geometries, e.g. for fluids at interfaces, as well as non-equilibrium molecular dynamics simulation of heat and mass transfer.

cs.CE↗

arXiv2010

Fast GPGPU Data Rearrangement Kernels using CUDA

Many high performance-computing algorithms are bandwidth limited, hence the need for optimal data rearrangement kernels as well as their easy integration into the rest of the application. In this work, we have built a CUDA library of fast kernels for a set of data rearrangement operations. In particular, we have built generic kernels for rearranging m dimensional data into n dimensions, including Permute, Reorder, Interlace/De-interlace, etc. We have also built kernels for generic Stencil computations on a two-dimensional data using templates and functors that allow application developers to rapidly build customized high performance kernels. All the kernels built achieve or surpass best-known performance in terms of bandwidth utilization.

cs.DC↗

arXiv2010

Efficient cosmological parameter sampling using sparse grids

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the likelihood-evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelised to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.

astro-ph.CO↗