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

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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

ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS VIA MAXIMAL REGULARITY

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arXiv 2024年

作者： Akrivis, Georgios Larsson, Stig Department of Computer Science and Engineering University of Ioannina Ioannina451 10 Greece Institute of Applied and Computational Mathematics FORTH Heraklion Crete700 13 Greece Department of Mathematical Sciences Chalmers University of Technology University of Gothenburg GothenburgSE–412 96 Sweden

We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge–Kutta methods for nonlinear parabolic equations;in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for nonautonomous linear parabolic *** Codes 65M12, 65M15, 65M60 © 2024, CC BY.

关键词： Galerkin methods

Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems

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arXiv 2024年

作者： Anandh, Thivin Ghose, Divij Jain, Himanshu Sunkad, Pratham Ganesan, Sashikumaar John, Volker Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore India Department of Mechanical Engineering Indian Institute of Technology Tamil Nadu Madras India Weierstrass Institute for Applied Analysis and Stochastics Berlin Germany Department of Mathematics and Computer Science Freie University Berlin Germany

This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature. © 2024, CC BY-NC-SA.

关键词： Stabilization

Dynamic model of a hyper-redundant, octopus-like manipulator for underwater applications

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Dynamic model of a hyper-redundant, octopus-like manipulator...

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

作者： Rongjie Kang Asimina Kazakidi Emanuele Guglielmino David T. Branson Dimitris P. Tsakiris John A. Ekaterinaris Darwin G. Caldwell Department of Advanced Robotics Istituto Italiano di Tecnologia Genova Italy Institute of Computer Science Foundation for Research and Technology Hellas FORTH Heraklion Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas FORTH Heraklion Greece

The octopus arm is a unique tool that combines strength and flexibility. It can shorten, elongate and bend at any point along its length. To model this behavior, a hyper-redundant manipulator composed of multiple segments is proposed. Each segment is a parallel robotic mechanism with redundant actuation. The kinematics and dynamics of this manipulator are analyzed and simulated utilizing a modular computational modeling method. Simulation results for some primitive movements are presented, and the effect of hydrodynamic forces is included.

关键词： Mathematical model Force Manipulator dynamics Joints Equations Pistons

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

Testing viable f(R) models with the angular-diameter distance to compact quasar cores

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Physical Review D 2019年第10期99卷 103505-103505页

作者： Joseph Sultana Fulvio Melia Demosthenes Kazanas Department of Mathematics Faculty of Science University of Malta Msida MSD2080 Malta Department of Physics The Applied Math Program and Department of Astronomy The University of Arizona Tucson Arizona 85721 USA Astrophysics Science Division NASA/Goddard Space Flight Center Greenbelt Maryland 20771 USA

We consider here some popular f(R) models generally viewed as possible alternatives to the existence of dark energy in General Relativity. For each of these, we compute the redshift zmax at which the angular diameter distance dA(z) is expected to reach its maximum value. This turning point in dA(z) was recently measured in a model-independent way using compact quasar cores and was found to occur at zmax=1.70±0.20. We compare the predictions of zmax for the f(R) models with this observed value to test their viability at a deeper level than has been attempted thus far, thereby quantifying an important observational difference between such modified gravity scenarios and standard Lambda Cold Dark Matter (ΛCDM) cosmology. Our results show that, while the most popular f(R) models today are consistent with this measurement to within 1σ, the turning point zmax will allow us to prioritize these alternative gravity theories as the measurement precision continues to improve, particularly with regard to how well they mitigate the tension between the predictions of ΛCDM and the observations. For example, while the Hu-Sawicki version of f(R) increases this tension, the Starobinky model reduces it.

关键词： Alternative gravity theories Cosmological parameters Relativistic aspects of cosmology

Development of a do-it-yourself (D.I.Y.) gel electrophoresis apparatus for Grade-12 STEM general biology students 2

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Development of a do-it-yourself (D.I.Y.) gel electrophoresis...

2nd International Annual Meeting on STEM Education, IAMSTEM 2019

作者： Gamale, Janne Noelle L. Acut, Dharel P. Niere, Karla Marie Frances P. Silagan, Gwen Stephany S. Curaraton, Ethel P. Latonio, Guadalupe C. Latonio, Rhett Anthony C. Magsayo, Joy R. High School Department Sotero B. Cabahug Forum for Literacy Consolacion Cebu6001 Philippines Applied Physics Program National Institute of Physics College of Science University of the Philippines - Diliman Roxas Ave. Diliman Quezon City1101 Philippines Science Education Program Graduate School College of Teacher Education Cebu Normal University Osmeña Blvd. Cebu City Cebu6000 Philippines Department of Science and Mathematics Education College of Education Mindanao State University - Iligan Institute of Technology Iligan City9200 Philippines

A hurdle to effective science education in schools is often the lack of teaching materials. Teaching science education in the 21st century requires direct visualization and manipulation with effective use and implementation for meaningful learning to occur, thus, unleashing students' potential towards the lesson, boosting their engagement in learning, and applying the knowledge into skills. This study was carried out to develop a do-it-yourself gel electrophoresis apparatus. This study was conducted in Cebu Normal University, Philippines with nineteen (19) teachers from the Methods of Teaching Science and Instructional Trends and Issues Class who evaluated the apparatus in terms of usability and functionality. The respondents tested the Gel Electrophoresis apparatus by conducting the experiment and they evaluated the apparatus' functionality and usability by using an evaluation sheet which is composed of eleven (11) usability questions, four (4) functionality questions. Suggestions were also asked to improve the said apparatus. After gathering data, the suggestions made by the respondents were incorporated which resulted to the improved D.I.Y. Gel Electrophoresis Apparatus. A manual with the procedures was also designed to further guide students and teachers on how to build the apparatus. With the findings and results obtained in the study, the respondents recommended the usage of the developed do-it-yourself gel electrophoresis apparatus in their respective classes and agreed that it is a good source of learning the concept of gel electrophoresis as a 21st century biological technique. The apparatus was easy to set-up and is of low-cost. During experimentation, the apparatus yielded with a positive result - the separation of food dyes which follows the principle of gel electrophoresis. Moreover, the experiment encourages creativity and it helps with the understanding of the nature of DNA and the concept of gel electrophoresis as a 21st century biological skills. ©

关键词： Students

Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography

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Advantage of Machine Learning over Maximum Likelihood in Lim...

IS and T International Symposium on Electronic Imaging: Machine Learning for Scientific Imaging, MLSI 2022

作者： Guo, Zhen Song, Jung Ki Barbastathis, George Glinsky, Michael E. Vaughan, Courtenay T. Larson, Kurt W. Alpert, Bradley K. Levine, Zachary H. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Department of Mechanical Engineering Massachusetts Institute of Technology CambridgeMA02139 United States Centre Singapore138002 Singapore Sandia National Laboratory AlbuquerqueNM87123 United States Applied and Computational Mathematics Division National Institute of Standards and Technology Boulder CO80305 United States Quantum Measurement Division National Institute of Standards and Technology GaithersburgMD20899 United States

Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks to determine and apply a prior distribution in the reconstruction process. Our neural networks learn the prior directly from synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the class of objects we are interested in reconstructing. In particular, we used deep generative models with 3D convolutional layers and 3D attention layers which are trained on 3D synthetic integrated circuit (IC) data from a model dubbed CircuitFaker. We demonstrate that, when the projection angles and photon budgets are limited, the priors from our deep generative models can dramatically improve the IC reconstruction quality on synthetic data compared with maximum likelihood estimation. Training the deep generative models with synthetic IC data from CircuitFaker illustrates the capabilities of the learned prior from machine learning. We expect that if the process were reproduced with experimental data, the advantage of the machine learning would persist. The advantages of machine learning in limited angle X-ray tomography may further enable applications in low-photon nanoscale imaging. © 2022, Society for Imaging Science and Technology

关键词： Photons

NUMERICAL NONLINEAR ALGEBRA

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arXiv 2023年

作者： Bates, Daniel J. Breiding, Paul Chen, Tianran Hauenstein, Jonathan D. Leykin, Anton Sottile, Frank Department of Mathematics U.S. Naval Academy 572C Holloway Road Mail Stop 9E AnnapolisMD21402 United States Universität Osnabrück FB Mathematik/Informatik Albrechtstr. 28a Osnabrück49076 Germany Department of Mathematics Auburn University at Montgomery MontgomeryAL36116 United States Department of Applied & Computational Mathematics & Statistics University of Notre Dame Notre DameIN46556 United States School of Mathematics Georgia Institute of Technology 686 Cherry Street AtlantaGA30332-0160 United States Department of Mathematics Texas A&M University College StationTX77843 United States

Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of Bézout. This was decisively linked to modern developments in algebraic geometry by the polyhedral homotopy algorithm of Huber and Sturmfels, which exploits the combinatorial structure of the equations and led to efficient software for solving polynomial equations. Subsequent growth of numerical nonlinear algebra continues to be informed by algebraic geometry and its applications. These include new approaches to solving, algorithms for studying positive-dimensional varieties, certification, and a range of applications both within mathematics and from other disciplines. With new implementations, numerical nonlinear algebra is now a fundamental computational tool for algebraic geometry and its applications. We survey some of these innovations and some recent *** Codes 14Q65, 65H14 Copyright © 2023, The Authors. All rights reserved.

关键词： Nonlinear equations