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HYPPO: A surrogate-based multi-level parallelism tool for hyperparameter optimization

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arXiv 2021年

作者： Dumont, Vincent Garner, Casey Trivedi, Anuradha Jones, Chelsea Ganapati, Vidya Mueller, Juliane Perciano, Talita Kiran, Mariam Day, Marc Computing Sciences Area Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics University of Minnesota Twin Cities Twin CitiesMN55414 United States Department of Biomedical Engineering Georgia Institute of Technology Emory University AtlantaGA30332 United States Department of Statistical Sciences & Operations Research Virginia Commonwealth University RichmondVA23284 United States Department of Engineering Swarthmore College SwarthmorePA19081 United States Computational Science Center National Renewable Energy Laboratory GoldenCO80401 United States

We present a new software, HYPPO, that enables the automatic tuning of hyperparameters of various deep learning (DL) models. Unlike other hyperparameter optimization (HPO) methods, HYPPO uses adaptive surrogate models and directly accounts for uncertainty in model predictions to find accurate and reliable models that make robust predictions. Using asynchronous nested parallelism, we are able to significantly alleviate the computational burden of training complex architectures and quantifying the uncertainty. HYPPO is implemented in Python and can be used with both TensorFlow and PyTorch libraries. We demonstrate various software features on time-series prediction and image classification problems as well as a scientific application in computed tomography image reconstruction. Finally, we show that (1) we can reduce by an order of magnitude the number of evaluations necessary to find the most optimal region in the hyperparameter space and (2) we can reduce by two orders of magnitude the throughput for such HPO process to complete. Copyright © 2021, The Authors. All rights reserved.

关键词： Python

Ab initio vibrational free energies including anharmonicity for multicomponent alloys

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npj computational Materials 2019年第1期5卷 454-459页

作者： Blazej Grabowski Yuji Ikeda Prashanth Srinivasan Fritz Körmann Christoph Freysoldt Andrew Ian Duff Alexander Shapeev Jörg Neugebauer Institute of Materials Science University of StuttgartPfaffenwaldring 5570569 StuttgartGermany Department for Computational Materials Design Max-Planck-Institut für Eisenforschung GmbHMax-Planck-Str.140237 DüsseldorfGermany Department of Materials Science and Engineering Delft University of TechnologyMekelweg 22628 CD DelftNetherlands Scientific Computing Department STFC Daresbury LaboratoryHartree CentreWarringtonUK Skolkovo Institute of Science and Technology Skolkovo Innovation CenterNobel St.3Moscow 143026Russia

The unique and unanticipated properties of multiple principal component alloys have reinvigorated the field of alloy design and drawn strong interest across scientific *** vast compositional parameter space makes these alloys a unique area of exploration by means of computational ***,as of now a method to compute efficiently,yet with high accuracy the thermodynamic properties of such alloys has been *** of the underlying reasons is the lack of accurate and efficient approaches to compute vibrational free energies—including anharmonicity—for these chemically complex multicomponent *** this work,a density-functional-theory based approach to overcome this issue is developed based on a combination of thermodynamic integration and a machine-learning *** demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.

关键词： alloys alloy thermodynamic

PowerNet: Efficient representations of polynomials and smooth functions by deep neural networks with rectified power units

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arXiv 2019年

作者： Li, Bo Tang, Shanshan Yu, Haijun Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 School OfMathematical Sciences University of Chinese Academy of Sciences Beijing100049 National Center ForMathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

MSC Codes 65M12, 65M15, 65P40Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations only when smoothness is not required. In this paper, we construct deep neural networks with rectified power units (RePU), which can give better approximations for smooth functions. Optimal algorithms are proposed to explicitly build neural networks with sparsely connected RePUs, which we call PowerNets, to represent polynomials with no approximation error. For general smooth functions, we first project the function to their polynomial approximations, then use the proposed algorithms to construct corresponding PowerNets. Thus, the error of best polynomial approximation provides an upper bound of the best RePU network approximation error. For smooth functions in higher dimensional Sobolev spaces, we use fast spectral transforms for tensor-product grid and sparse grid discretization to get polynomial approximations. Our constructive algorithms show clearly a close connection between spectral methods and deep neural networks: a PowerNet with n layers can exactly represent polynomials up to degree sn, where s is the power of RePUs. The proposed PowerNets have potential applications in the situations where high-accuracy is desired or smoothness is required. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

Better approximations of high dimensional smooth functions by deep neural networks with rectified power units

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arXiv 2019年

作者： Li, Bo Tang, Shanshan Yu, Haijun NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China China Justice Big Data Institute Beijing100043 China

MSC Codes 65D15, 65M12, 65M15Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to their universal representation power and successful applications. Some theoretical progress regarding the approximation power of deep ReLU network for functions in Sobolev space and Korobov space have recently been made by [D. Yarotsky, Neural Network, 94:103-114, 2017] and [H. Montanelli and Q. Du, SIAM J Math. Data Sci., 1:78-92, 2019], etc. In this paper, we show that deep networks with rectified power units (RePU) can give better approximations for smooth functions than deep ReLU networks. Our analysis bases on classical polynomial approximation theory and some efficient algorithms proposed in this paper to convert polynomials into deep RePU networks of optimal size with no approximation error. Comparing to the results on ReLU networks, the sizes of RePU networks required to approximate functions in Sobolev space and Korobov space with an error tolerance Ε, by our constructive proofs, are in general O(log1Ε ) times smaller than the sizes of corresponding ReLU networks constructed in most of the existing literature. Comparing to the classical results of Mhaskar [Mhaskar, Adv. Comput. Math. 1:61-80, 1993], our constructions use less number of activation functions and numerically more stable, they can be served as good initials of deep RePU networks and further trained to break the limit of linear approximation theory. The functions represented by RePU networks are smooth functions, so they naturally fit in the places where derivatives are involved in the loss function. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

Color dependence of the topological susceptibility in Yang-Mills theories

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arXiv 2022年

作者： Bennett, Ed Hong, Deog Ki Lee, Jong-Wan David Lin, C.-J. Lucini, Biagio Piai, Maurizio Vadacchino, Davide Swansea Academy of Advanced Computing Swansea University Fabian Way Wales SwanseaSA1 8EN United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Center for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Physics Division National Centre for Theoretical Sciences Taipei10617 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Wales SwanseaSA1 8EN United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Wales SwanseaSA2 8PP United Kingdom School of Mathematics Hamilton Mathematics Institute Trinity College Dublin 2 Ireland Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

For Yang-Mills theories in four dimensions, we propose to rescale the ratio between topological susceptibility and string tension squared in a universal way, dependent only on group factors. We apply this suggestion to SU(Nc) and Sp(Nc) groups, and compare lattice measurements performed by several independent collaborations. We show that the two sequences of (rescaled) numerical results in these two families of groups are compatible with each other. We hence perform a combined fit, and extrapolate to the common large-Nc limit. © 2022, CC BY.

关键词： Topology

GWSurrogate: A Python package for gravitational wave surrogate models

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arXiv 2025年

作者： Field, Scott E. Varma, Vijay Blackman, Jonathan Gadre, Bhooshan Galley, Chad R. Islam, Tousif Mitman, Keefe Pürrer, Michael Ravichandran, Adhrit Scheel, Mark A. Stein, Leo C. Yoo, Jooheon Department of Mathematics Center for Scientific Computing & Data Science Research University of Massachusetts DartmouthMA02747 United States Theoretical Astrophysics 350-17 California Institute of Technology PasadenaCA91125 United States Utrecht University Utrecht3584 CC Netherlands Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics Center for Computational Research East Hall University of Rhode Island KingstonRI02881 United States Department of Physics and Astronomy The University of Mississippi UniversityMS38677 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States

Gravitational waves are ripples in space-time caused by the motion of massive objects. One of the most astrophysically important sources of gravitational radiation is caused by two orbiting compact objects, such as black holes and neutron stars, that slowly inspiral and merge. The motion of these massive objects generates gravitational waves that radiate to the far field where gravitational-wave detectors can observe them. Complicated partial or ordinary differential equations govern the entire process. Traditionally, the dynamics of compact binary systems and the emitted gravitational waves have been computed by expensive simulation codes that can take days to months to run. A key simulation output is the gravitational wave signal for a particular set of parameter values describing the system, such as the black holes’ masses and spins. The computed signal is required for a diverse range of multiple-query applications, such as template bank generation for searches, parameter estimation, mock data analysis, studies of model bias, and tests of general relativity, to name a few. In such settings, the high-fidelity signal computed from differential equations is often too slow to be directly used. Surrogate models offer a practical way to dramatically accelerate model evaluation while retaining the high-fidelity accuracy of the expensive simulation code;an example is shown in Fig. 1. Surrogate models can be constructed in various ways, but what separates these models from other modeling frameworks is that they are primarily data-driven. Given a training set of gravitational waveform data sampling the parameter space, a model is built by following three steps: 1. Feature extraction: the waveform is decomposed into data pieces that are simple to model, 2. Dimensionality reduction: each data piece is approximated by a low-dimensional vector space, which reduces the degrees of freedom we need to model, and 3. Regression: fitting and regression techniques are applied to the l

关键词： Gravitational effects

Is there evidence for exponential quantum advantage in quantum chemistry?

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arXiv 2022年

作者： Lee, Seunghoon Lee, Joonho Zhai, Huanchen Tong, Yu Dalzell, Alexander M. Kumar, Ashutosh Helms, Phillip Gray, Johnnie Cui, Zhi-Hao Liu, Wen-Yuan Kastoryano, Michael Babbush, Ryan Preskill, John Reichman, David R. Campbell, Earl T. Valeev, Edward F. Lin, Lin Chan, Garnet Kin-Lic Division of Chemistry and Chemical Engineering California Institute of Technology PasadenaCA91125 United States Department of Chemistry Columbia University New YorkNY10027 United States Department of Mathematics University of California BerkeleyCA94720 United States Aws Center for Quantum Computing PasadenaCA91125 United States Department of Chemistry Virginia Tech BlacksburgVA24061 United States Amazon Quantum Solutions Lab SeattleWA98170 United States Google Quantum AI 340 Main Street VeniceCA90291 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States Riverlane Cambridge United Kingdom

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential "killer application" [1, 2, 3, 4, 5]. Indications of potential exponential quantum advantage in artificial tasks [6, 7, 8, 9] have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem. © 2022, CC BY.

关键词： Quantum chemistry

Sp(2N) Yang-Mills theories on the lattice: scale setting and topology

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arXiv 2022年

作者： Bennett, Ed Hong, Deog Ki Lee, Jong-Wan Lin, C.-J. David Lucini, Biagio Piai, Maurizio Vadacchino, Davide Swansea Academy of Advanced Computing Swansea University Fabian Way Swansea WalesSA1 8EN United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Center for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Physics Division National Centre for Theoretical Sciences Taipei10617 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea WalesSA1 8EN United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea WalesSA2 8PP United Kingdom School of Mathematics Hamilton Mathematics Institute Trinity College Dublin 2 Ireland Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

We study Yang-Mills lattice theories with Sp(Nc) gauge group, with Nc = 2N, for N = 1, ···, 4. We show that if we divide the renormalised couplings appearing in the Wilson flow by the quadratic Casimir C2(F) of the Sp(Nc) group, then the resulting quantities display a good agreement among all values of Nc considered, over a finite interval in flow time. We use this scaled version of the Wilson flow as a scale-setting procedure, compute the topological susceptibility of the Sp(Nc) theories, and extrapolate the results to the continuum limit for each Nc. © 2022, CC BY.

关键词： Lattice theory

Two-grid based adaptive proper orthogonal decomposition algorithm for time dependent partial differential equations

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arXiv 2019年

作者： Dai, Xiaoying Kuang, Xiong Xin, Jack Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics University of California at Irvine IrvineCA92697 United States

In this article, we propose a two-grid based adaptive proper orthogonal decomposition(POD) algorithm to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for the numerical solution obtained in the fine grid. Our new algorithm is cheap and easy to implement. We implement our new method to the solution of time-dependent advection-diffusion equations with Kolmogorov flow and ABC flow. The numerical results show that our method is more efficient than the existing POD algorithms. Copyright © 2019, The Authors. All rights reserved.

关键词： Principal component analysis