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arXiv 2024年

作者： Li, Yanhua Ouyang, Xiaocao Pan, Chaofan Zhang, Jie Zhao, Sen Xia, Shuyin Yang, Xin Wang, Guoyin Li, Tianrui School of Computing and Artificial Intelligence Southwestern University of Finance and Economics Chengdu611130 China Engineering Research Center of Intelligent Finance Ministry of Education Chengdu611130 China Key Laboratory of Big Data Intelligent Computing Chongqing Key Laboratory of Computational Intelligence Chongqing University of Posts and Telecommunications Chongqing400065 China National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China School of Computing and Artificial Intelligence Southwest Jiaotong University Chengdu611756 China

Open intent classification is critical for the development of dialogue systems, aiming to accurately classify known intents into their corresponding classes while identifying unknown intents. Prior boundary-based methods assumed known intents fit within compact spherical regions, focusing on coarse-grained representation and precise spherical decision boundaries. However, these assumptions are often violated in practical scenarios, making it difficult to distinguish known intent classes from unknowns using a single spherical boundary. To tackle these issues, we propose a Multi-granularity Open intent classification method via adaptive Granular-Ball decision boundary (MOGB). Our MOGB method consists of two modules: representation learning and decision boundary acquiring. To effectively represent the intent distribution, we design a hierarchical representation learning method. This involves iteratively alternating between adaptive granular-ball clustering and nearest sub-centroid classification to capture fine-grained semantic structures within known intent classes. Furthermore, multi-granularity decision boundaries are constructed for open intent classification by employing granular-balls with varying centroids and radii. Extensive experiments conducted on three public datasets demonstrate the effectiveness of our proposed method. Copyright © 2024, The Authors. All rights reserved.

关键词： Semantics

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arXiv

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arXiv 2022年

作者： Belitsky, A.V. Smirnov, A.V. Smirnov, V.A. Department of Physics Arizona State University TempeAZ85287-1504 United States Research Computing Center Moscow State University Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia Skobeltsyn Institute of Nuclear Physics Moscow State University Moscow Center for Fundamental and Applied Mathematics Moscow119992 Russia

We address the problem of evaluation of multiloop Feynman integrals by means of their Mellin-Barnes representation. After a brief overview of available capabilities though open source toolkits and their application in various circumstances, we introduce a new code MBcreate which allows one to automatically deduce a concise Mellin-Barnes representation for a given parametric integral. A thorough discussion of its implementation and use is provided. Copyright © 2022, The Authors. All rights reserved.

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An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable Lévy noise

arXiv

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arXiv 2022年

作者： Fang, Cheng Lu, Yubin Gao, Ting Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, lots of log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios which could have high error and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by α-stable Lévy noise from only random pairwise data. Our innovations include: (1) designing a deep learning approach to learn both drift and diffusion coefficients for Lévy induced noise with α across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, (3) proposing an end-to-end complete framework for stochastic systems identification under a general input data assumption, that is, α-stable random variable. Finally, numerical experiments and comparisons with the nonlocal Kramers-Moyal formulas with moment generating function confirm the effectiveness of our method. Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

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PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval

arXiv

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arXiv 2023年

作者： Liu, Aoxu Fan, Xiaohong Yang, Yin Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the Key Laboratory of Intelligent Computing & Information Processing the Ministry of Education Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the National Center for Applied Mathematics in Hunan Xiangtan411105 China

The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are based on black-box network models that lack interpretability and plug-and-play (PnP) frameworks that are computationally complex and require careful parameter tuning. To address this, we have developed PRISTA-Net, a deep unfolding network (DUN) based on the first-order iterative shrinkage thresholding algorithm (ISTA). This network utilizes a learnable nonlinear transformation to address the proximal-point mapping sub-problem associated with the sparse priors, and an attention mechanism to focus on phase information containing image edges, textures, and structures. Additionally, the fast Fourier transform (FFT) is used to learn global features to enhance local information, and the designed logarithmic-based loss function leads to significant improvements when the noise level is low. All parameters in the proposed PRISTA-Net framework, including the nonlinear transformation, threshold parameters, and step size, are learned end-to-end instead of being manually set. This method combines the interpretability of traditional methods with the fast inference ability of deep learning and is able to handle noise at each iteration during the unfolding stage, thus improving recovery quality. Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that our approach outperforms the existing state-of-the-art methods in terms of qualitative and quantitative evaluations. Our source codes are available at https://***/liuaxou/PRISTA-Net. Copyright © 2023, The Authors. All rights reserved.

关键词： Mapping

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Precompactness in bivariate metric semigroup-valued bounded variation spaces

arXiv

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arXiv 2025年

作者： Niu, Yinglian Xu, Jingshi School of Mathematics and Computing Science Guilin University of Electronic Technology 1 Jinjilu Guangxi Guilin541004 China Center for Applied Mathematics of Guangxi Guilin University of Electronic Technology 1 Jinjilu Guangxi Guilin541004 China Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology 1 Jinjilu Guangxi Guilin541004 China

In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded Wiener variation spaces, bounded Waterman variation spaces, bounded Riesz variation spaces and bounded Korenblum variation spaces. To do so, we introduce the concept of equimetric *** Codes 26A45, 54E50 Copyright © 2025, The Authors. All rights reserved.

关键词： Vector spaces

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Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics

arXiv

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arXiv 2023年

作者： Chertock, Alina Kurganov, Alexander Redle, Michael Zeitlin, Vladimir Department of Mathematics Center for Research in Scientific Computing North Carolina State University RaleighNC27695 United States Department of Mathematics Shenzhen International Center for Mathematics Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and Technology Shenzhen518055 China Applied and Computational Mathematics RWTH Aachen University Aachen52062 Germany Department of Mathematics North Carolina State University RaleighNC27695 United States CNRS Paris75231 France Shenzhen International Center for Mathematics Southern University of Science and Technology Shenzhen518055 China

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in [A. Chertock, A. Kurganov, M. Redle, and K. Wu, ArXiv preprint (2022), arXiv:2212.02682]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirm the lack of spurious oscillations, robustness, and high resolution of the obtained results. © 2023, CC BY.

关键词： Magnetohydrodynamics

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Scalable method for Bayesian experimental design without integrating over posterior distribution

arXiv

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arXiv 2023年

作者： Hoang, Vinh Espath, Luis Krumscheid, Sebastian Tempone, Raúl Mathematics for Uncertainty Quantification RWTH Aachen University Germany Faculty of Science University of Nottingham United Kingdom Steinbuch Center for Computing Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76131 Germany Computer Electrical and Mathematical Sciences and Engineering KAUST Alexander von Humboldt professor in Mathematics of Uncertainty Quantification RWTH Aachen University Germany

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate. A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design. This criterion seeks the optimal experimental design by minimizing the expected conditional variance, which is also known as the expected posterior variance. This study presents a novel likelihood-free approach to the A-optimal experimental design that does not require sampling or integrating the Bayesian posterior distribution. Our proposed approach is developed based on two properties of the conditional expectation: the law of total variance and the property of orthogonal projection. The expected conditional variance is obtained via the variance of the conditional expectation using the law of total variance, and we take advantage of the orthogonal projection property to approximate the conditional expectation. We derive an asymptotic error estimation for the proposed estimator of the expected conditional variance and show that the intractability of the posterior distribution does not affect the performance of our approach. We use an artificial neural network (ANN) to approximate the nonlinear conditional expectation in the implementation of our method. We then extend our approach for dealing with the case that the domain of experimental design parameters is continuous by integrating the training process of the ANN into minimizing the expected conditional variance. Specifically, we propose a nonlocal approximation of the conditional expectation and apply transfer learning to reduce the number of evaluations of the observation model. Through numerical experiments, we demonstrate that our method greatly reduces the number of observation model evaluations compared with widely used importance sampling-based approaches. This reduction is c

关键词： Design of experiments

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Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics

SSRN

引用

SSRN 2023年

作者： Chertock, Alina Kurganov, Alexander Redle, Michael Zeitlin, Vladimir Department of Mathematics Center for Research in Scientific Computing North Carolina State University RaleighNC27695 United States Department of Mathematics Shenzhen International Center for Mathematics Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and Technology Shenzhen518055 China Applied and Computational Mathematics RWTH Aachen University Aachen52062 Germany Department of Mathematics North Carolina State University RaleighNC27695 United States CNRS Paris 75231 France Shenzhen International Center for Mathematics Southern University of Science and Technology Shenzhen518055 China

关键词： Magnetohydrodynamics

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Can AI weather models predict out-of-distribution gray swan tropical cyclones?

arXiv

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arXiv 2024年

作者： Sun, Y. Qiang Hassanzadeh, Pedram Zand, Mohsen Chattopadhyay, Ashesh Weare, Jonathan Abbot, Dorian S. University of Chicago Department of the Geophysical Sciences ChicagoIL60637 United States University of Chicago Committee on Computational and Applied Mathematics ChicagoIL60637 United States University of Chicago Research Computing Center ChicagoIL60637 United States University of California Department of Applied Mathematics Santa CruzCA95064 United States New York University Courant Institute of Mathematical Sciences New YorkNY10012 United States

Predicting gray swan weather extremes, which are possible but so rare that they are absent from the training dataset, is a major concern for AI weather/climate models. An important open question is whether AI models can extrapolate from weaker weather events present in the training set to stronger, unseen weather extremes. To test this, we train independent versions of the AI model FourCastNet on the 1979-2015 ERA5 dataset with all data, or with Category 3-5 tropical cyclones (TCs) removed, either globally or only over the North Atlantic or Western Pacific basin. We then test these versions of FourCastNet on 2018-2023 Category 5 TCs (gray swans). All versions yield similar accuracy for global weather, but the one trained without Category 3-5 TCs cannot accurately forecast Category 5 TCs, indicating that these models cannot extrapolate from weaker storms. The versions trained without Category 3-5 TCs in one basin show some skill forecasting Category 5 TCs in that basin, suggesting that FourCastNet can generalize across tropical basins. This is encouraging and surprising because regional information is implicitly encoded in inputs. No version satisfies gradient-wind balance, implying that enforcing such physical constraints may not improve generalizability to gray swans. Given that current state-of-the-art AI weather/climate models have similar learning strategies, we expect our findings to apply to other models and extreme events. Our work demonstrates that novel learning strategies are needed for AI weather/climate models to provide early warning or estimated statistics for the rarest, most impactful weather extremes. © 2024, CC BY-NC-SA.

关键词： Tropical cyclone

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State-space models are accurate and efficient neural operators for dynamical systems

arXiv

引用

arXiv 2024年

作者： Hu, Zheyuan Daryakenari, Nazanin Ahmadi Shen, Qianli Kawaguchi, Kenji Em Karniadakis, George Department of Computer Science National University of Singapore Singapore119077 Singapore Center for Biomedical Engineering School of Engineering Brown University ProvidenceRI02912 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation, to name a few. To this end, this paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning. Mamba addresses the limitations of existing architectures by dynamically capturing long-range dependencies and enhancing computational efficiency through reparameterization techniques. To extensively test Mamba and compare against another 11 baselines, we introduce several strict extrapolation testbeds that go beyond the standard interpolation benchmarks. We demonstrate Mamba’s superior performance in both interpolation and challenging extrapolation tasks. Mamba consistently ranks among the top models while maintaining the lowest computational cost and exceptional extrapolation capabilities. Moreover, we demonstrate the good performance of Mamba for a real-world application in quantitative systems pharmacology for assessing the efficacy of drugs in tumor growth under limited data scenarios. Taken together, our findings highlight Mamba’s potential as a powerful tool for advancing scientific machine learning in dynamical systems modeling. (The code will be available at https://***/zheyuanhu01/State_ Space_Model_Neural_Operator upon acceptance.) © 2024, CC BY.

关键词： Recurrent neural networks

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