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Rehme","Fabian Franzelin","Dirk Pflüger" ], "authors": [ {"first" : "Michael F.", "last" : "Rehme"}, {"first" : "Fabian", "last" : "Franzelin"}, {"first" : "Dirk", "last" : "Pflüger"} ], "abstract": "Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. 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Rehme","Dirk Pflüger" ], "authors": [ {"first" : "Michael F.", "last" : "Rehme"}, {"first" : "Dirk", "last" : "Pflüger"} ], "abstract": "B-splines on sparse grids are a versatile method for higher-dimensional approximation, especially in smooth settings or if gradient information is advantageous. With increasing dimension, grid points on the boundary become prohibitively expensive and have to be avoided. To compensate for the missing boundary points, the basis functions are typically modified according to natural boundary conditions. However, the resulting splines do not span the polynomial space anymore. In this work we introduce extended B-splines that are based on the polynomial basis property. We apply them on spatially adaptive sparse grids. 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Rehme","Fabian Franzelin","Dirk Pflüger" ], "authors": [ {"first" : "Michael F.", "last" : "Rehme"}, {"first" : "Fabian", "last" : "Franzelin"}, {"first" : "Dirk", "last" : "Pflüger"} ], "abstract": "Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.", "bibtexKey": "rehme2019bsplines" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/28b341984a107175be05eebdda39e6c12/clausbraun", "tags" : [ "AxC","CCG","PCG","SimTech","approximate","computing","conjugate","error-correction","error-detection","fault-tolerance","gradient","linear","myown","preconditioned","solver","sparse","systems" ], "intraHash" : "8b341984a107175be05eebdda39e6c12", "interHash" : "819e882fc0ec03e0c6e332411bfbf42d", "label" : "Applying Efficient Fault Tolerance to Enable the Preconditioned Conjugate Gradient Solver on Approximate Computing Hardware", "user" : "clausbraun", "description" : "", "date" : "2018-03-19 16:15:07", "changeDate" : "2018-03-19 15:34:51", "count" : 6, "pub-type": "inproceedings", "booktitle": "Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'16)", "year": "2016", "url": "", "author": [ "Alexander Schöll","Claus Braun","Hans-Joachim Wunderlich" ], "authors": [ {"first" : "Alexander", "last" : "Schöll"}, {"first" : "Claus", "last" : "Braun"}, {"first" : "Hans-Joachim", "last" : "Wunderlich"} ], "pages": "21-26","abstract": "A new technique is presented that allows to execute the preconditioned conjugate gradient (PCG) solver on approximate hardware while ensuring correct solver results. This technique expands the scope of approximate computing to scientific and engineering applications. The changing error resilience of PCG during the solving process is exploited by different levels of approximation which trade off numerical accuracy and hardware utilization. Such approximation levels are determined at runtime by periodically estimating the error resilience. An efficient fault tolerance technique allows reductions in hardware utilization by ensuring the continued exploitation of maximum allowed energy-accuracy trade-offs. Experimental results show that the hardware utilization is reduced on average by 14.5% and by up to 41.0% compared to executing PCG on accurate hardware.", "file" : "http://www.iti.uni-stuttgart.de/fileadmin/rami/files/publications/2016/DFT_SchoeBW2016.pdf", "doi" : "http://dx.doi.org/10.1109/DFT.2016.7684063", "bibtexKey": "SchoeBW2016" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/28c90a682adda1e125eb007f0c70bd70a/clausbraun", "tags" : [ "ABFT","CG","PCG","SimTech","conjugate","error","error-correction","error-detection","fault","fault-tolerance","gradient","linear","myown","preconditioned","solver","sparse","system" ], "intraHash" : "8c90a682adda1e125eb007f0c70bd70a", "interHash" : "d133c0d9eda7017c266a9d01721a9c91", "label" : "Low-Overhead Fault-Tolerance for the Preconditioned Conjugate Gradient Solver", "user" : "clausbraun", "description" : "", "date" : "2018-03-19 16:15:07", "changeDate" : "2018-03-19 15:33:36", "count" : 6, "pub-type": "inproceedings", "booktitle": "Proceedings of the International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT'15)", "year": "2015", "url": "", "author": [ "Alexander Schöll","Claus Braun","Michael A. Kochte","Hans-Joachim Wunderlich" ], "authors": [ {"first" : "Alexander", "last" : "Schöll"}, {"first" : "Claus", "last" : "Braun"}, {"first" : "Michael A.", "last" : "Kochte"}, {"first" : "Hans-Joachim", "last" : "Wunderlich"} ], "pages": "60-65","abstract": "Linear system solvers are an integral part for many different compute-intensive applications and they benefit from the compute power of heterogeneous computer architectures. However, the growing spectrum of reliability threats for such nano-scaled CMOS devices makes the integration of fault tolerance mandatory. The preconditioned conjugate gradient (PCG) method is one widely used solver as it finds solutions typically faster compared to direct methods. Although this iterative approach is able to tolerate certain errors, latest research shows that the PCG solver is still vulnerable to transient effects. Even single errors, for instance, caused by marginal hardware, harsh environments, or particle radiation, can considerably affect execution times, or lead to silent data corruption. In this work, a novel fault-tolerant PCG solver with extremely low runtime overhead is proposed. Since the error detection method does not involve expensive operations, it scales very well with increasing problem sizes. In case of errors, the method selects between three different correction methods according to the identified error. Experimental results show a runtime overhead for error detection ranging only from 0.04% to 1.70%.", "file" : "http://www.iti.uni-stuttgart.de/fileadmin/rami/files/publications/2015/DFTS_SchoeBKW2015.pdf", "doi" : "http://dx.doi.org/10.1109/DFT.2015.7315136", "bibtexKey": "SchoeBKW2015a" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/27e5f4629e5616459c867bc30d3893e78/clausbraun", "tags" : [ "ABFT","CG","PCG","SimTech","conjugate","efficiency","fault","fault-tolerance","gradient","linear","myown","preconditioned","solver","sparse" ], "intraHash" : "7e5f4629e5616459c867bc30d3893e78", "interHash" : "7911878633d0e9fce50d136187cf87a4", "label" : "Efficient On-Line Fault-Tolerance for the Preconditioned Conjugate Gradient Method", "user" : "clausbraun", "description" : "", "date" : "2018-03-19 16:15:07", "changeDate" : "2018-03-19 15:30:49", "count" : 6, "pub-type": "inproceedings", "booktitle": "Proceedings of the 21st IEEE International On-Line Testing Symposium (IOLTS'15)", "year": "2015", "url": "", "author": [ "Alexander Schöll","Claus Braun","Michael A. Kochte","Hans-Joachim Wunderlich" ], "authors": [ {"first" : "Alexander", "last" : "Schöll"}, {"first" : "Claus", "last" : "Braun"}, {"first" : "Michael A.", "last" : "Kochte"}, {"first" : "Hans-Joachim", "last" : "Wunderlich"} ], "pages": "95--100","abstract": "Linear system solvers are key components of many scientific applications and they can benefit significantly from modern heterogeneous computer architectures. However, such nano-scaled CMOS devices face an increasing number of reliability threats, which make the integration of fault tolerance mandatory. The preconditioned conjugate gradient method (PCG) is a very popular solver since it typically finds solutions faster than direct methods, and it is less vulnerable to transient effects. However, as latest research shows, the vulnerability is still considerable. Even single errors caused, for instance, by marginal hardware, harsh operating conditions or particle radiation can increase execution times considerably or corrupt solutions without indication. In this work, a novel and highly efficient fault-tolerant PCG method is presented. The method applies only two inner products to reliably detect errors. In case of errors, the method automatically selects between roll-back and efficient on-line correction. This significantly reduces the error detection overhead and expensive re-computations.", "file" : "http://www.iti.uni-stuttgart.de/fileadmin/rami/files/publications/2015/IOLTS_SchoeBKW2015.pdf", "doi" : "http://dx.doi.org/10.1109/IOLTS.2015.7229839", "bibtexKey": "SchoeBKW2015" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2973313fa8f49996637b903eadac4fc19/clausbraun", "tags" : [ "ABFT","SimTech","algebra","error-detection","fault-tolerance","linear","localization","myown","online","sparse" ], "intraHash" : "973313fa8f49996637b903eadac4fc19", "interHash" : "3e8ca3c5bdad028a00edd6b200f98b53", "label" : "Efficient Algorithm-Based Fault Tolerance for Sparse Matrix Operations", "user" : "clausbraun", "description" : "", "date" : "2018-03-19 16:15:07", "changeDate" : "2018-03-19 15:26:03", "count" : 6, "pub-type": "inproceedings", "booktitle": "Proceedings of the 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'16)", "year": "2016", "url": "", "author": [ "Alexander Schöll","Claus Braun","Michael A. Kochte","Hans-Joachim Wunderlich" ], "authors": [ {"first" : "Alexander", "last" : "Schöll"}, {"first" : "Claus", "last" : "Braun"}, {"first" : "Michael A.", "last" : "Kochte"}, {"first" : "Hans-Joachim", "last" : "Wunderlich"} ], "pages": "251--262","abstract": "We propose a fault tolerance approach for sparse matrix operations that detects and implicitly locates errors in the results for efficient local correction. This approach reduces the runtime overhead for fault tolerance and provides high error coverage. Existing algorithm-based fault tolerance approaches for sparse matrix operations detect and correct errors, but they often rely on expensive error localization steps. General checkpointing schemes can induce large recovery cost for high error rates. For sparse matrix-vector multiplications, experimental results show an average reduction in runtime overhead of 43.8%, while the error coverage is on average improved by 52.2% compared to related work. The practical applicability is demonstrated in a case study using the iterative Preconditioned Conjugate Gradient solver. When scaling the error rate by four orders of magnitude, the average runtime overhead increases only by 31.3% compared to low error rates.", "file" : "http://www.iti.uni-stuttgart.de/fileadmin/rami/files/publications/2016/DSN_SchoeBKW2016.pdf", "doi" : "http://dx.doi.org/10.1109/DSN.2016.31", "bibtexKey": "SchoeBKW2016" } ] }