We present a generator of virtual molecules that selects valid chem- istry on the basis of the octet rule. Also, we introduce a mesomer group key that allows a fast detection of duplicates in the generated *** to exis...
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To predict the quality of a process outcome with given process parameters in real-time, surrogate models are often adopted. A surrogate model is a statistical model that interpolates between data points obtained eithe...
To predict the quality of a process outcome with given process parameters in real-time, surrogate models are often adopted. A surrogate model is a statistical model that interpolates between data points obtained either by process measurements or deterministic models of the process. However, in manufacturing processes the amount of useful data is often limited, and therefore setting up a sufficiently accurate surrogate model is challenging. The present contribution shows how to handle limited data in a surrogate modeling approach using the example of a cup drawing process. The purpose of the surrogate model is to classify the quality of the drawn cup and to predict its final geometry. These classification and regression tasks are solved via machine learning methods. The training data is sampled on a relatively wide range varying three parameters of a finite element simulation, namely sheet metal thickness, blank holder force, and friction. The geometrical features of the cup are extracted using domain knowledge. Besides this knowledge-based approach, an outlook is given for a data-driven surrogate modeling approach.
In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is non-intrusive ...
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Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, spa...
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(纸本)9783319381534
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the curse of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
Quantum mechanical calculations require the repeated solution of a Schrödinger equation for the wavefunctions of the system, from which materials properties follow. Recent work has shown the effectiveness of enri...
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Quantum mechanical calculations require the repeated solution of a Schrödinger equation for the wavefunctions of the system, from which materials properties follow. Recent work has shown the effectiveness of enriched finite element type Galerkin methods at significantly reducing the degrees of freedom required to obtain accurate solutions. However, time to solution has been adversely affected by the need to solve a generalized rather than standard eigenvalue problem and the ill-conditioning of associated systems matrices. In this work, we address both issues by proposing a stable and efficient orbital-enriched partition of unity method to solve the Schrödinger boundary-value problem in a parallelepiped unit cell subject to Bloch-periodic boundary conditions. In the proposed partition of unity method, the three-dimensional domain is covered by overlapping patches, with a compactly-supported weight function associated with each patch. A key ingredient in our approach is the use of non-negative weight functions that possess the flat-top property, i.e., each weight function is identically equal to unity over some finite subset of its support. This flattop property provides a pathway to devise a stable approximation over the whole domain. On each patch, we use p-th degree orthogonal (Legendre) polynomials that ensure p-th order completeness, and in addition include eigenfunctions of the radial Schrödinger equation. Furthermore, we adopt a variational lumping approach to construct a (block-)diagonal overlap matrix that yields a standard eigenvalue problem for which there exist efficient eigensolvers. The accuracy, stability, and efficiency of the proposed method is demonstrated for the Schrödinger equation with a harmonic potential as well as a localized Gaussian potential. We show that the proposed approach delivers optimal rates of convergence in the energy, and the use of orbital enrichment significantly reduces the number of degrees of freedom for a given desired accu
ATK-ForceField is a software package for atomistic simulations using classical interatomic potentials. It is implemented as a part of the Atomistix ToolKit (ATK), which is a Python programming environment that makes i...
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In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathe...
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Cross-sectoral coupling of energy systems could provide the necessary flexibility for future energy systems with a high share of renewable energies. The gas grid implies large storage capacities and thus promises an e...
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Cross-sectoral coupling of energy systems could provide the necessary flexibility for future energy systems with a high share of renewable energies. The gas grid implies large storage capacities and thus promises an economically attractive balance for fluctuating energy sources. A benchmark gas distribution network, coupled to the CIGRE benchmark network for electricity is presented within this paper, to universally investigate the impacts on gas grid infrastructure. The network includes interconnected meshed and radial topologies for both low and medium pressure gas networks. They have been synthesized from existing real networks in cooperation with the Rheinische NETZGesellschaft mbH. Applications range from analyzing network impacts of widespread CHP or fuel cell implementation, over comparing the cost-effectiveness of different future pathways between expansion and decommissioning of the gas grid network, to analyzing the impacts of distributed injection of renewable gas. The overall aim is to build a complete network benchmark for an integral cross-sectoral energy system including also heat.
Quantitative remote sensing retrieval algorithms help understanding the dynamic aspects of Digital ***,the Big Data and complex models in Digital Earth pose grand challenges for computation *** this article,taking the...
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Quantitative remote sensing retrieval algorithms help understanding the dynamic aspects of Digital ***,the Big Data and complex models in Digital Earth pose grand challenges for computation *** this article,taking the aerosol optical depth(AOD)retrieval as a study case,we exploit parallel computing methods for high efficient geophysical parameter *** present an efficient geocomputation workflow for the AOD calculation from the Moderate Resolution Imaging Spectroradiometer(MODIS)satellite *** to their individual potential for parallelization,several procedures were adapted and implemented for a successful parallel execution on multicore processors and Graphics Processing Units(GPUs).The benchmarks in this paper validate the high parallel performance of the retrieval workflow with speedups of up to 5.x on a multi-core processor with 8 threads and 43.x on a *** specifically address the time-consuming model retrieval part,hybrid parallel patterns which combine the multicore processor’s and the GPU’s compute power were implemented with static and dynamic workload distributions and evaluated on two systems with different CPU–GPU *** is shown that only the dynamic hybrid implementation leads to a greatly enhanced overall exploitation of the heterogeneous hardware environment in varying circumstances.
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