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Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

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arXiv 2024年

作者： Wang, Kesen Kim, Minwoo Castruccio, Stefano Genton, Marc G. Statistics Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics Pusan National University Busan46241 Korea Republic of Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model. © 2024, CC BY.

关键词： Clean energy

Few-photon single ionization of cold rubidium in the over-the-barrier regime

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Physical Review A 2023年第3期107卷 033114-033114页

作者： Huanyu Ma Xincheng Wang Linxuan Zhang Zhihan Zou Junyang Yuan Yixuan Ma Rujin Lv Zhenjie Shen Tianmin Yan Matthias Weidemüller Difa Ye Yuhai Jiang Center for Transformative Science and School of Physical Science and Technology ShanghaiTech University Shanghai 201210 China Shanghai Advanced Research Institute Chinese Academy of Sciences Shanghai 201210 China School of Future Technology University of Chinese Academy of Sciences Beijing 100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100193 China Physikalisches Institut Universität Heidelberg Im Neuenheimer Feld 226 69120 Heidelberg Germany

Photoionization of rubidium atoms cooled in a magneto-optical trap, characterized by the coexistence of the ground 5S1/2 and excited 5P3/2 states, is investigated experimentally and theoretically with the 400-nm femtosecond laser pulses at intensities of I=(3×109)–(4.5×1012) W/cm2. The recoil-ion momentum distribution (RIMD) of Rb+ exhibits rich ringlike structures and their energies correspond to one-photon ionization of the 5P3/2 state and two-photon and three-photon ionizations of the 5S1/2 state, respectively. With increasing I, the dips near zero momentum (NZM) in the experimental RIMDs become shallow dramatically and their peaked Rb+ momenta ionized from the 5P3/2 state move obviously toward zero while the peaks from the 5S1/2 state do not shift. In addition, the ion-yield ratio of the 5S1/2 state to the 5P3/2 state varies from I to I1.5 as I increases. These features indicate a transition from perturbative ionization to strongly perturbative ionization for the 5P3/2 state. Numerical simulations by solving the time-dependent Schrödinger equation (TDSE) can qualitatively explain the measurements of the RIMD, photoion angular distributions, and ion-yield ratio. However, some discrepancies still exist, especially for the NZM dip, which could stem from the electron-electron correlation that is neglected in the present TDSE simulations since we have adopted the single-active-electron approximation.

关键词： Atomic & molecular processes in external fields Multiphoton or tunneling ionization & excitation Single- and few-photon ionization & excitation

Stationary rotating strings as relativistic particle mechanics

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Physical Review D 2008年第2期78卷 023525-023525页

作者： Kouji Ogawa Hideki Ishihara Hiroshi Kozaki Hiroyuki Nakano Shinya Saito Department of Mathematics and Physics Graduate School of Science Osaka City University Osaka 558-8585 Japan Department of Applied Chemistry and Biotechnology Niigata Institute of Technology Kashiwazaki Niigata 945-1195 Japan Center for Computational Relativity and Gravitation School of Mathematical Sciences Rochester Institute of Technology Rochester New York 14623 USA

Stationary rotating strings can be viewed as geodesic motions in appropriate metrics in two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have infinite length with various wiggly shapes. Averaged value of the string energy, the angular momentum, and the linear momentum along the string are discussed.

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Geometry-based data generation

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arXiv 2018年

作者： Lindenbaum, Ofir Stanley, Jay S. Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New HavenCT United States Applied Mathematics Program Yale University New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States

We propose a new type of generative model of high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, and improves several downstream data analysis tasks such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations and reveal intrinsic patterns and mutual-information relationships between genes on a single cell dataset of hematopoiesis. Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

Reliable Extrapolation of Deep Neural Operators Informed by Physics or Sparse Observations

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SSRN

SSRN 2023年

作者： Zhu, Min Zhang, Handi Jiao, Anran Karniadakis, George Em Lu, Lu Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer and Information Science University of Pennsylvania PhiladelphiaPA19104 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States School of Engineering Brown University ProvidenceRI02912 United States

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information-the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. © 2023, The Authors. All rights reserved.

关键词： Extrapolation

Quantum interference of Glory rescattering in strong-field atomic ionization

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arXiv 2017年

作者： Xia, Q.Z. Tao, J.F. Cai, J. Fu, L.B. Liu, J. National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Physics and Electronic Engineering Jiangsu Normal University Xuzhou221116 China Graduate School China Academy of Engineering Physics Beijing100088 China CAPT HEDPS IFSA Collaborative Innovation Center of MoE Peking University Beijing100871 China

During the ionization of atoms irradiated by linearly polarized intense laser fields, we find for the first time that the transverse momentum distribution of photoelectrons can be well fitted by a squared zeroth-order Bessel function because of the quantum interference effect of Glory rescattering. The characteristic of the Bessel function is determined by the common angular momentum of a bunch of semiclassical paths termed as Glory trajectories, which are launched with different nonzero initial transverse momenta distributed on a specific circle in the momentum plane and finally deflected to the same asymptotic momentum, which is along the polarization direction, through post-tunneling rescattering. Glory rescattering theory (GRT) based on the semiclassical path-integral formalism is developed to address this effect quantitatively. Our theory can resolve the long-standing discrepancies between existing theories and experiments on the fringe location, predict the sudden transition of the fringe structure in holographic patterns, and shed light on the quantum interference aspects of low-energy structures in strong-field atomic ionization. Copyright © 2017, The Authors. All rights reserved.

关键词： Quantum interference phenomena

Reliable extrapolation of deep neural operators informed by physics or sparse observations

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arXiv 2022年

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new behavior of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. © 2022, CC BY-NC-ND.

关键词： Extrapolation

Bayesian Formulations for Graph Spectral Denoising

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arXiv 2023年

作者： Leone, Sam Sun, Xingzhi Perlmutter, Michael Krishnaswamy, Smita Program for Applied Mathematics Yale University United States Department of Computer Science Yale University United States Department of Mathematics Boise State University United States Department of Genetics Yale School of Medicine United States Wu Tsai Institute Yale University United States FAIR Meta AI United States Computational Biology and Bioinformatics Program Yale University United States

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms' ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data. © 2023, CC BY.

关键词： Frequency domain analysis

Effect of imperfections on the hyperuniformity of many-body systems

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Physical Review B 2018年第5期97卷 054105-054105页

作者： Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

A hyperuniform many-body system is characterized by a structure factor Sk that vanishes in the small-wave-number limit or equivalently by a local number variance σN2R associated with a spherical window of radius R that grows more slowly than Rd in the large-R limit. Thus, the hyperuniformity implies anomalous suppression of long-wavelength density fluctuations relative to those in typical disordered systems, i.e., σN2R∼Rd as R→∞. Hyperuniform systems include perfect crystals, quasicrystals, and special disordered systems. Disordered hyperuniform systems are amorphous states of matter that lie between a liquid and crystal [S. Torquato et al., Phys. Rev. X 5, 021020 (2015)], and have been the subject of many recent investigations due to their novel properties. In the same way that there is no perfect crystal in practice due to the inevitable presence of imperfections, such as vacancies and dislocations, there is no “perfect” hyperuniform system, whether it is ordered or not. Thus, it is practically and theoretically important to quantitatively understand the extent to which imperfections introduced in a perfectly hyperuniform system can degrade or destroy its hyperuniformity and corresponding physical properties. This paper begins such a program by deriving explicit formulas for Sk in the small-wave-number regime for three types of imperfections: (1) uncorrelated point defects, including vacancies and interstitials, (2) stochastic particle displacements, and (3) thermal excitations in the classical harmonic regime. We demonstrate that our results are in excellent agreement with numerical simulations. We find that “uncorrelated” vacancies or interstitials destroy hyperuniformity in proportion to the defect concentration p. We show that “uncorrelated” stochastic displacements in perfect lattices can never destroy the hyperuniformity but it can be degraded such that the perturbed lattices fall into class III hyperuniform systems, where σN2R∼Rd−α as R→∞ and 0<α<1. By cont

关键词： Interstitials Structural properties Vacancies