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arXiv 2022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 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

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Numerical evidence against advantage with quantum fidelity kernels on classical data

arXiv

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arXiv 2022年

作者： Slattery, Lucas Shaydulin, Ruslan Chakrabarti, Shouvanik Pistoia, Marco Khairy, Sami Wild, Stefan M. Department of Physics University of Illinois Urbana-Champaign ChampaignIL61820 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Global Technology Applied Research JPMorgan Chase New YorkNY10017 United States

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well-aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential "flattening" of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well-approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

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Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

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Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials

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Dose Requirements for Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1968-1969页

作者： Manassa, Jason Schwartz, Jonathan Jiang, Yi Zheng, Huihuo Fessler, Jeffrey A. Wendy Di, Zichao Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Advanced Photon Source Facility Argonne National Laboratory Lemont IL United States Argonne Leadership Computing Facility Argonne National Laboratory Lemont IL United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Applied Physics Program University of Michigan Ann Arbor MI United States

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Unbiased Estimation using a Class of Diffusion Processes

arXiv

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arXiv 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 KSA Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (d, B(d)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}tϵ[0,1]on d, d ϵ 0. This latter process is constructed such that, starting at X0= 0, one has X1∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ > 0, the associated cost is O(ϵ-5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ-2| log(ϵ)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion

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Extended Fayans energy density functional: optimization and analysis

arXiv

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arXiv 2024年

作者： Reinhard, Paul-Gerhard O'Neal, Jared Wild, Stefan M. Nazarewicz, Witold Institut für Theoretische Physik II Universität Erlangen-Nürnberg ErlangenD-91058 Germany Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Industrial Engineering and Management Sciences Northwestern University EvanstonIL60208 United States Facility for Rare Isotope Beams Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even-even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity. Copyright © 2024, The Authors. All rights reserved.

关键词： Density functional theory

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Sparse-grid Discontinuous Galerkin Methods for the Vlasov–Poisson–Lenard–Bernstein Model

arXiv

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arXiv 2024年

作者： Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D. Green, David L. Snyder, Phil Canik, John Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Fusion Energy Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Department of Mathematics University of Tennessee KnoxvilleTN37996 United States Type One Energy Group Oak RidgeTN37830 United States Commonwealth Scientific and Industrial Research Organisation Mayfield WestNSW2304 Australia

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD. Copyright © 2024, The Authors. All rights reserved.

关键词： Integral equations

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Multiregion Multiscale Image Segmentation with Anisotropic Diffusion 25th

Multiregion Multiscale Image Segmentation with Anisotropic D...

引用

25th International Conference on Pattern Recognition Workshops, ICPR 2020

作者： Prasath, V. B. Surya Thanh, Dang Ngoc Hoang Hai, Nguyen Hoang Dvoenko, Sergey Department of Electrical Engineering and Computer Science University of Cincinnati CincinnatiOH45221 United States Division of Biomedical Informatics Cincinnati Children’s Hospital Medical Center CincinnatiOH45229 United States Department of Biomedical Informatics College of Medicine University of Cincinnati CincinnatiOH45267 United States Department of Pediatrics University of Cincinnati College of Medicine CincinnatiOH45257 United States Department of Information Technology School of Business Information Technology University of Economics Ho Chi Minh City Ho Chi Minh City Viet Nam Department of Computer Science Vietnam-Korea University of Information and Communication Technology – The University of Danang Danang Viet Nam Department of Information Security Institute of Applied Mathematics and Computer Science Tula State University Tula city Russia

ISBN: (纸本)9783030688202

We present a multiregion image segmentation approach which utilizes multiscale anisotropic diffusion based scale spaces. By combining powerful edge preserving anisotropic diffusion smoothing with isolevel set linking and merging, we obtain coherent segments which are tracked across multiple scales. A hierarchical tree representation of the given input image with progressively simplified regions is used with intra-scale splitting and inter-scale merging for obtaining multiregion segmentations. Experimental results on natural and medical images indicate that multiregion, multiscale image segmentation (MMIS) approach obtains coherent segmentation results. © 2021, Springer Nature Switzerland AG.

关键词： Diffusion

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Tumor Detection, Segmentation and Classification Challenge on Automated 3D Breast Ultrasound: The TDSC-ABUS Challenge

arXiv

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arXiv 2025年

作者： Luo, Gongning Xu, Mingwang Chen, Hongyu Liang, Xinjie Tao, Xing Ni, Dong Jeong, Hyunsu Kim, Chulhong Stock, Raphael Baumgartner, Michael Kirchhoff, Yannick Rokuss, Maximilian Maier-Hein, Klaus Yang, Zhikai Fan, Tianyu Boutry, Nicolas Tereshchenko, Dmitry Moine, Arthur Charmetant, Maximilien Sauer, Jan Du, Hao Bai, Xiang-Hui Raikar, Vipul Pai Montoya-Del-Angel, Ricardo Martí, Robert Luna, Miguel Lee, Dongmin Qayyum, Abdul Mazher, Moona Guo, Qihui Wang, Changyan Awasthi, Navchetan Zhao, Qiaochu Wang, Wei Wang, Kuanquan Wang, Qiucheng Dong, Suyu School of Computer Science and Technology Harbin Institute of Technology Harbin150001 China Department of Mathematics Faculty of Science National University of Singapore Singapore National-Regional Key Technology Engineering Laboratory for Medical Ultrasound School of Biomedical Engineering Shenzhen University Medical School Shenzhen University Shenzhen China Laboratory Shenzhen University Shenzhen China School of Biomedical Engineering and Informatics Nanjing Medical University Nanjing China Pohang Korea Republic of Heidelberg Division of Medical Image Computing Heidelberg Germany Faculty of Mathematics and Computer Science Heidelberg University Germany Heidelberg Germany HIDSS4Health - Helmholtz Information and Data Science School for Health Karlsruhe Heidelberg Germany Pattern Analysis and Learning Group Department of Radiation Oncology Heidelberg University Hospital Germany Department of Biomedical Engineering and Health KTH Royal Institute of Technology Stockholm Sweden France FathomX Singapore Saw Swee Hock School of Public Health National University of Singapore Singapore Philips Research University of Girona Spain Department of Robotics and Mechatronics Engineering DGIST Korea Republic of Department of Interdisciplinary Studies of Artificial Intelligence DGIST Korea Republic of National Heart and Lung Institute Faculty of Medicine Imperial College London London United Kingdom Centre for Medical Image Computing Department of Computer Science University College London London United Kingdom Lab School of Communication and Information Engineering Shanghai University Shanghai China Faculty of Science Mathematics and Computer Science Informatics Institute University of Amsterdam Amsterdam1090 GH Netherlands Department of Biomedical Engineering and Physics Amsterdam UMC Amsterdam1081 HV Netherlands Xi’an Jiaotong-Liverpool University China Department of Ultrasound Harbin Medical University Cancer Hospital No. 150 Haping Road Nangang

Breast cancer is one of the most common causes of death among women worldwide. Early detection helps in reducing the number of deaths. Automated 3D Breast Ultrasound (ABUS) is a newer approach for breast screening, which has many advantages over handheld mammography such as safety, speed, and higher detection rate of breast cancer. Tumor detection, segmentation, and classification are key components in the analysis of medical images, especially challenging in the context of 3D ABUS due to the significant variability in tumor size and shape, unclear tumor boundaries, and a low signal-to-noise ratio. The lack of publicly accessible, well-labeled ABUS datasets further hinders the advancement of systems for breast tumor analysis. Addressing this gap, we have organized the inaugural Tumor Detection, Segmentation, and Classification Challenge on Automated 3D Breast Ultrasound 2023 (TDSC-ABUS2023). This initiative aims to spearhead research in this field and create a definitive benchmark for tasks associated with 3D ABUS image analysis. In this paper, we summarize the top-performing algorithms from the challenge and provide critical analysis for ABUS image examination. We offer the TDSC-ABUS challenge as an open-access platform at https://***/ to benchmark and inspire future developments in1algorithmic research. © 2025, CC BY.

关键词： Image segmentation

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Theory for Equivariant Quantum Neural Networks

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PRX Quantum 2024年第2期5卷 020328-020328页

作者： Quynh T. Nguyen Louis Schatzki Paolo Braccia Michael Ragone Patrick J. Coles Frédéric Sauvage Martín Larocca M. Cerezo Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Information Sciences Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana Illinois 61801 USA Dipartimento di Fisica e Astronomia Università di Firenze Sesto Fiorentino Florence 50019 Italy Department of Mathematics University of California Davis Davis California 95616 USA Center for Nonlinear Studies Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

Quantum neural network architectures that have little to no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks the action of which commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a comprehensive theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group. We develop multiple methods to construct equivariant layers for EQNNs and analyze their advantages and drawbacks. Our methods can find unitary or general equivariant quantum channels efficiently even when the symmetry group is exponentially large or continuous. As a special implementation, we show how standard quantum convolutional neural networks (QCNNs) can be generalized to group-equivariant QCNNs where both the convolution and pooling layers are equivariant to the symmetry group. We then numerically demonstrate the effectiveness of a SU(2)-equivariant QCNN over symmetry-agnostic QCNN on a classification task of phases of matter in the bond-alternating Heisenberg model. Our framework can be readily applied to virtually all areas of quantum machine learning. Lastly, we discuss about how symmetry-informed models such as EQNNs provide hopes to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity.

关键词： Machine learning Quantum algorithms & computation

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