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arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization

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Sharp composition bounds for gaussian differential privacy via edgeworth expansion

arXiv

引用

arXiv 2020年

作者： Zheng, Qinqing Dong, Jinshuo Long, Qi Su, Weijie J. Department of Statistics Graduate Group in Applied Mathematics and Computational Science Department of Biostatistics Epidemiology and Informatics

Datasets containing sensitive information are often sequentially analyzed by many algorithms. This raises a fundamental question in differential privacy regarding how the overall privacy bound degrades under composition. To address this question, we introduce a family of analytical and sharp privacy bounds under composition using the Edgeworth expansion in the framework of the recently proposed f-differential privacy. In contrast to the existing composition theorems using the central limit theorem, our new privacy bounds under composition gain improved tightness by leveraging the refined approximation accuracy of the Edgeworth expansion. Our approach is easy to implement and computationally efficient for any number of compositions. The superiority of these new bounds is confirmed by an asymptotic error analysis and an application to quantifying the overall privacy guarantees of noisy stochastic gradient descent used in training private deep neural networks. Copyright © 2020, The Authors. All rights reserved.

关键词： Deep neural networks

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Correction: Unbiased and multilevel methods for a class of diffusions partially observed via marked point processes

引用

Statistics and Computing 2024年第6期34卷 1-1页

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

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WONDER: weighted one-shot distributed ridgeregression in high dimensions

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2020年第1期21卷 2483-2534页

作者： Edgar Dobriban Yue Sheng Wharton Statistics Department University of Pennsylvania Philadelphia PA Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA

In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high-dimensional random-effects model where each predictor has a small effect, we discover several new ***-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call "infinite-worker limit".Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are *** also propose a new Weighted ONe-shot DistributEd Ridge regression algorithm (WONDER). We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.

关键词： distributed learning ridge regression high-dimensional statistics random matrix theory

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Disk2Planet: A Robust and Automated Machine Learning Tool for Parameter Inference in Disk-Planet Systems

arXiv

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arXiv 2024年

作者： Mao, Shunyuan Dong, Ruobing Yi, Kwang Moo Lu, Lu Wang, Sifan Perdikaris, Paris Department of Physics and Astronomy University of Victoria VictoriaBCV8P 5C2 Canada Kavli Institute for Astronomy and Astrophysics Peking University Beijing100871 China Department of Computer Science University of British Columbia VancouverBCV6T 1Z4 Canada Department of Statistics and Data Science Yale University New HavenCT06511 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Institute for Foundations of Data Science Yale University New HavenCT06520 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

We introduce Disk2Planet, a machine learning-based tool to infer key parameters in disk-planet systems from observed protoplanetary disk structures. Disk2Planet takes as input the disk structures in the form of two-dimensional density and velocity maps, and outputs disk and planet properties, that is, the Shakura-Sunyaev viscosity, the disk aspect ratio, the planet-star mass ratio, and the planet's radius and azimuth. We integrate the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), an evolutionary algorithm tailored for complex optimization problems, and the Protoplanetary Disk Operator Network (PPDONet), a neural network designed to predict solutions of disk-planet interactions. Our tool is fully automated and can retrieve parameters in one system in three minutes on an Nvidia A100 graphics processing unit. We empirically demonstrate that our tool achieves percent-level or higher accuracy, and is able to handle missing data and unknown levels of noise. Copyright © 2024, The Authors. All rights reserved.

关键词： Open source software

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A deep potential model with long-range electrostatic interactions

arXiv

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

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Ecumenical Modal Logic 1

引用

3rd International Workshop on Dynamic Logic, DaLí 2020

作者： Marin, Sonia Pereira, Luiz Carlos Pimentel, Elaine Sales, Emerson Department of Computer Science University College London London United Kingdom Philosophy Department PUC-Rio Rio de Janeiro Brazil Department of Mathematics UFRN Natal Brazil Graduate Program in Applied Mathematics and Statistics UFRN Natal Brazil

ISBN: (数字)9783030658403

ISBN: (纸本)9783030658397

The discussion about how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz’ system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In this work we extend Prawitz’ ecumenical idea to alethic K -modalities. © 2020, Springer Nature Switzerland AG.

关键词： Computer circuits

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Chiral Quasi-Bound States in the Continuum

引用

Physical Review Letters 2021年第7期126卷 073001-073001页

作者： Adam Overvig Nanfang Yu Andrea Alù Photonics Initiative Advanced Science Research Center at the Graduate Center of the City University of New York New York New York 10031 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Physics Program Graduate Center City University of New York New York New York 10016 USA

Quasi-bound states in the continuum (QBICs) are Fano resonant states with long optical lifetimes controlled by symmetry-breaking perturbations. While conventional Fano responses are limited to linear polarizations and do not support tailored phase control, here we introduce QBICs born of chiral perturbations that encode arbitrary elliptical polarization states and enable geometric phase engineering. We thereby design metasurfaces with ultrasharp spectral features that shape the impinging wave front with near-unity efficiency. Our findings extend Fano resonances beyond their conventional limits, opening opportunities for nanophotonics, classical and quantum optics, and acoustics.

关键词： Metamaterials Photonic crystals

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Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties

arXiv

引用

arXiv 2023年

作者： Morse, Peter K. Kim, Jaeuk Steinhardt, Paul J. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k| → 0;and stealthy hyperuniform systems have S(k) = 0 for the finite range 0 30 for systems sizes more than an order of magnitude larger. We further show that this ultra-high accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small. © 2023, CC BY.

关键词： Physical properties

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Forecasting high-frequency spatio-temporal wind power with dimensionally reduced echo state networks

arXiv

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arXiv 2021年

作者： Huang, Huang Castruccio, Stefano Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal 23955-6900 Saudi Arabia Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

Fast and accurate hourly forecasts of wind speed and power are crucial in quan-tifying and planning the energy budget in the electric grid. Modeling wind at a high resolution brings forth considerable challenges given its turbulent and highly nonlin-ear dynamics. In developing countries, where wind farms over a large domain are currently under construction or consideration, this is even more challenging given the necessity of modeling wind over space as well. In this work, we propose a machine learning approach to model the nonlinear hourly wind dynamics in Saudi Arabia with a domain-specific choice of knots to reduce the spatial dimensionality. Our re-sults show that for locations highlighted as wind abundant by a previous work, our approach results in an 11% improvement in the two-hour-ahead forecasted power against operational standards in the wind energy sector, yielding a saving of nearly one million US dollars over a year under current market prices in Saudi Arabia. © 2021, CC BY.

关键词： Wind power

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