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Surrogate-data-enriched Physics-Aware Neural Networks

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arXiv 2021年

作者： Leiteritz, Raphael Buchfink, Patrick Haasdonk, Bernard Pflüger, Dirk Institute for Parallel and Distributed Systems University of Stuttgart Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Germany

Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to additionally respect data from numerical simulations or experiments in the training process. However, this data is frequently expensive to obtain and thus only scarcely available for complex models. In this work, we investigate how physics-aware models can be enriched with computationally cheaper, but inexact, data from other surrogate models like Reduced-Order Models (ROMs). In order to avoid trusting too-low-fidelity surrogate solutions, we develop an approach that is sensitive to the error in inexact data. As a proof of concept, we consider the one-dimensional wave equation and show that the training accuracy is increased by two orders of magnitude when inexact data from ROMs is incorporated. © 2021, CC BY.

关键词： Data reduction

parallel machine learning of partial differential equations

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arXiv 2021年

作者： Totounferoush, Amin Pour, Neda Ebrahimi Roller, Sabine Mehl, Miriam Institute for Parallel and Distributed Systems University of Stuttgart Germany Chair of Simulation Techniques and Scientific Computing University of Siegen Germany

In this work1, we present a parallel scheme for machine learning of partial differential equations. The scheme is based on the decomposition of the training data corresponding to spatial subdomains, where an individual neural network is assigned to each data subset. Message Passing Interface (MPI) is used for parallelization and data communication. We use convolutional neural network layers (CNN) to account for spatial connectivity. We showcase the learning of the linearized Euler equations to assess the accuracy of the predictions and the efficiency of the proposed scheme. These equations are of particular interest for aeroacoustic problems. A first investigation demonstrated a very good agreement of the predicted results with the simulation results. In addition, we observe an excellent reduction of the training time compared to the sequential version, providing an almost perfect scalability up to 64 CPU cores. Copyright © 2021, The Authors. All rights reserved.

关键词： Convolution

Robust Recurrent Neural Network to Identify Ship Motion in Open Water with Performance Guarantees - Technical Report

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arXiv 2022年

作者： Frank, Daniel Latif, Decky Aspandi Muehlebach, Michael Unger, Benjamin Staab, Steffen Institute for Parallel and Distributed Systems University of Stuttgart Germany Max Planck Institute for Intelligent Systems Germany Stuttgart Center for Simulation Science Germany Institute for Parallel and Distributed Systems University of Stuttgart and Electronics and Computer Science University of Southampton United Kingdom

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this work, we represent a recurrent neural network as a linear time-invariant system with nonlinear disturbances. By introducing constraints on the parameters, we can guarantee finite gain stability and incremental finite gain stability. We apply this identification method to learn the motion of a four-degrees-of-freedom ship that is moving in open water and compare it against other purely learning-based approaches with unconstrained parameters. Our analysis shows that the constrained recurrent neural network has a lower prediction accuracy on the test set, but it achieves comparable results on an out-of-distribution set and respects stability conditions. © 2022, CC BY.

关键词： Recurrent neural networks

Partitioning parallel simulation of wireless networks

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Partitioning parallel simulation of wireless networks

simulation Winter Conference

作者： A. Boukerche A. Fabbri Parallel Simulation and Distributed Systems PARADISE Research Laboratory Department of Computer Science University of North Texas Denton TX USA

We present a simulation testbed for wireless and mobile telecommunication systems, a two-stage PCS parallel simulation testbed which makes use of a conservative scheme at stage 1, and of time warp at stage 2. While time warp is considered to be an effective synchronization mechanism in parallel and distributed discrete event simulation (PDES) it is also well known for its instability due to rollbacks and its devastating effect, i.e., series of cascading rollbacks, among other factors. Thus, our primary goal is to study the impact and the importance of partitioning in our PCS model while reducing significantly the number of rollbacks.

关键词： Wireless networks Personal communication networks Time warp simulation Computational modeling System testing Solid modeling Telecommunication traffic Traffic control Memory management Computer simulation

B-Splines for Sparse Grids: Algorithms and Application to Higher-Dimensional Optimization

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arXiv 2019年

作者： Valentin, Julian Simulation Software Engineering Institute for Parallel and Distributed Systems University of Stuttgart Universitätsstr. 38 Stuttgart70569 Germany

In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality, rendering them infeasible if the parameter domain of the function is higher-dimensional (four or more parameters). Sparse grids constitute a discretization method that drastically eases the curse, while the approximation quality deteriorates only insignificantly. However, conventional basis functions such as piecewise linear functions are not smooth (continuously differentiable). Hence, these basis functions are unsuitable for applications in which gradients are required. One example for such an application is gradient-based optimization, in which the availability of gradients greatly improves the speed of convergence and the accuracy of the results. This thesis demonstrates that hierarchical B-splines on sparse grids are well-suited for obtaining smooth interpolants for higher dimensionalities. The thesis is organized in two main parts: In the first part, we derive new B-spline bases on sparse grids and study their implications on theory and algorithms. In the second part, we consider three real-world applications in optimization: topology optimization, biomechanical continuum-mechanics, and dynamic portfolio choice models in finance. The results reveal that the optimization problems of these applications can be solved accurately and efficiently with hierarchical B-splines on sparse grids. Copyright © 2019, The Authors. All rights reserved.

关键词： Interpolation

An adaptive partitioning algorithm for conservative parallel simulation

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An adaptive partitioning algorithm for conservative parallel...

International Symposium on parallel and distributed Processing (IPDPS)

作者： A. Boukerche Parallel Simulation and Distributed Systems PARADISE Research Laboratory Department of Computer Sciences University of North Texas Denton TX USA

Enabling interactive mobile simulations through distributed reduced models

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arXiv 2018年

作者： Dibaka, Christoph Haasdonkb, Bernard Schmidtb, Andreas Durra, Frank Rothermela, Kurt Institute of Parallel and Distributed Systems University of Stuttgart Stuttgart Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany

Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between the mobile device and a remote server based on the reduced basis method. Evaluations show that we can speed-up the numerical computation by over 131 times while using 73 times less energy. Copyright © 2018, The Authors. All rights reserved.

关键词： Augmented reality

Server-assisted interactive mobile simulations for pervasive applications

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Server-assisted interactive mobile simulations for pervasive...

IEEE International Conference on Pervasive Computing and Communications (PerCom)

作者： Christoph Dibak Andreas Schmidt Frank Dürr Bernard Haasdonk Kurt Rothermel Institute of Parallel and Distributed Systems University of Stuttgart Stuttgart Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany

ISBN: (纸本)9781509043286

Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between mobile device and a remote server. For the computation of parameter-dependent solutions of the simulation, we use the reduced basis method, which allows to drastically reduce the computation time and energy consumption. We present three approaches for the distributed execution of the reduced basis method between mobile device and server. Evaluations show that we can speed-up the numerical computation to over 131 times while using 73 times less energy compared to offloading everything to a server.

关键词： Training Production facilities Servers

Exahd: An exa-scalable two-level sparse grid approach for higher-dimensional problems in plasma physics and beyond

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Exahd: An exa-scalable two-level sparse grid approach for hi...

International Workshop on parallel Processing, Euro-Par 2014

作者： Pflüger, Dirk Heene, Mario Bungartz, Hans-Joachim Kowitz, Christoph Hinojosa, Alfredo Parra Griebel, Michael Zaspel, Peter Jenko, Frank Dannert, Tilman Institute for Parallel and Distributed Systems University of Stuttgart Germany Chair of Scientific Computing Technische Universität München Germany Institute for Numerical Simulation University of Bonn Germany Max Planck Institute for Plasma Physics Germany Computing Centre of the Max Planck Society and the MPI for Plasma Physics Germany

ISBN: (纸本)9783319143125

High-dimensional problems pose a challenge for tomorrow’s supercomputing. Problems that require the joint discretization of more dimensions than space and time are among the most compute-hungry ones and thus standard candidates for exascale computing and even beyond. This project tackles such problems by a hierarchical extrapolation approach, the sparse grid combination technique. The method not only enables their treatment in the first place. The hierarchical approach also provides novel ways to deal with central problems in high-performance computing such as scalability and resilience: Global communication can be avoided and reduced to a small subset, and faults can be compensated for without the need for recomputations or checkpoint-restart. As an exemplary prototype for high-dimensional problems, turbulence simulations in plasma physics are studied. ©Springer International Publishing Switzerland 2014.

关键词： Computers