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Register a new userAdaptive Multigrid Strategy for Large-scale Molecular Mechanics Optimization
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In this paper, we present an efficient adaptive multigrid strategy for large-scale molecular mechanics optimization. The oneway multigrid method is used with inexact approximations, such as the quasi-atomistic (QA) approximation or the blended ghost force correction (BGFC) approximation on each coarse level, combined with adaptive mesh refinements based on the gradient-based a posteriori error estimator. For crystalline defects, like vacancies, micro-crack and dislocation, sublinear complexity is observed numerically when the adaptive BGFC method is employed. For systems with more than ten millions atoms, this strategy has a fivefold acceleration in terms of CPU time.
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Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. In this work, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the Ptychographic Iterative Engine (PIE), a workhorse in the optics community.
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower the computational demands significantly. However, for effects that intrinsically depend on particle size, coarse grain models fail to correctly predict the behaviour of the granular system. To solve this problem we have developed a new technique based on the efficient combination of fine-scale and coarse grain DEM models. The method is designed to capture the details of the granular system in spatially confined sub-regions while keeping the computational benefits of the coarse grain model where a lower resolution is sufficient. To this end, our method establishes two-way coupling between resolved and coarse grain parts of the system by volumetric passing of boundary conditions. Even more, multiple levels of coarse-graining may be combined to achieve an optimal balance between accuracy and speedup. This approach enables us to reach large time and length scales while retaining specifics of crucial regions. Furthermore, the presented model can be extended to coupled CFD-DEM simulations, where the resolution of the CFD mesh may be changed adaptively as well.
We present details of our implementation of the Wuppertal adaptive algebraic multigrid code DD-$alpha$AMG on SIMD architectures, with particular emphasis on the Intel Xeon Phi processor (KNC) used in QPACE 2. As a smoother, the algorithm uses a domain-decomposition-based solver code previously developed for the KNC in Regensburg. We optimized the remaining parts of the multigrid code and conclude that it is a very good target for SIMD architectures. Some of the remaining bottlenecks can be eliminated by vectorizing over multiple test vectors in the setup, which is discussed in the contribution of Daniel Richtmann.
Distributed optimization for solving non-convex Optimal Power Flow (OPF) problems in power systems has attracted tremendous attention in the last decade. Most studies are based on the geographical decomposition of IEEE test systems for verifying the feasibility of the proposed approaches. However, it is not clear if one can extrapolate from these studies that those approaches can be applied to very large-scale real-world systems. In this paper, we show, for the first time, that distributed optimization can be effectively applied to a large-scale real transmission network, namely, the Polish 2383-bus system for which no pre-defined partitions exist, by using a recently developed partitioning technique. More specifically, the problem solved is the AC OPF problem with geographical decomposition of the network using the Alternating Direction Method of Multipliers (ADMM) method in conjunction with the partitioning technique. Through extensive experimental results and analytical studies, we show that with the presented partitioning technique the convergence performance of ADMM can be improved substantially, which enables the application of distributed approaches on very large-scale systems.
Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each type of functions, which makes it difficult to exploit the structure of the problem and utilize the vast amount of existing algorithms. In this paper, we propose a simple strategy for universal online convex optimization, which avoids these limitations. The key idea is to construct a set of experts to process the original online functions, and deploy a meta-algorithm over the emph{linearized} losses to aggregate predictions from experts. Specifically, we choose Adapt-ML-Prod to track the best expert, because it has a second-order bound and can be used to leverage strong convexity and exponential concavity. In this way, we can plug in off-the-shelf online solvers as black-box experts to deliver problem-dependent regret bounds. Furthermore, our strategy inherits the theoretical guarantee of any expert designed for strongly convex functions and exponentially concave functions, up to a double logarithmic factor. For general convex functions, it maintains the minimax optimality and also achieves a small-loss bound.
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