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Unsupervised Feature Based Algorithms for Time Series Extrinsic Regression

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arXiv 2023年

作者： Guijo-Rubio, David Middlehurst, Matthew Arcencio, Guilherme Silva, Diego Furtado Bagnall, Anthony Department of Computer Science and Numerical Analysis University of Cordoba Cordoba14071 Spain School of Computing Sciences University of East Anglia Norfolk Norwich United Kingdom Department of Computing Universidade Federal de São Carlos São Carlos Brazil Institute of Mathematics and Computer Sciences Universidade de São Paulo São Paulo Brazil

Time Series Extrinsic Regression (TSER) involves using a set of training time series to form a predictive model of a continuous response variable that is not directly related to the regressor series. The TSER archive for comparing algorithms was released in 2022 with 19 problems. We increase the size of this archive to 63 problems and reproduce the previous comparison of baseline algorithms. We then extend the comparison to include a wider range of standard regressors and the latest versions of TSER models used in the previous study. We show that none of the previously evaluated regressors can outperform a regression adaptation of a standard classifier, rotation forest. We introduce two new TSER algorithms developed from related work in time series classification. FreshPRINCE is a pipeline estimator consisting of a transform into a wide range of summary features followed by a rotation forest regressor. DrCIF is a tree ensemble that creates features from summary statistics over random intervals. Our study demonstrates that both algorithms, along with InceptionTime, exhibit significantly better performance compared to the other 18 regressors tested. More importantly, these two proposals (DrCIF and FreshPRINCE) models are the only ones that significantly outperform the standard rotation forest regressor. © 2023, CC BY.

关键词： Time series

On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

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arXiv 2018年

作者： Schroeder, Philipp W. John, Volker Lederer, Philip L. Lehrenfeld, Christoph Lube, Gert Schöberl, Joachim Institute for Numerical and Applied Mathematics Georg-August-Universität Göttingen Göttingen37083 Germany Weierstrass Institute for Applied Analysis and Stochastics Berlin10117 Germany Department of Mathematics and Computer Science Freie Universität Berlin Berlin14195 Germany Institute for Analysis and Scientific Computing TU Wien 1040 Wien Austria

Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin–Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed. Copyright © 2018, The Authors. All rights reserved.

关键词： numerical methods

Probabilistic computation underlying sequence learning in a spiking attractor memory network

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BMC Neuroscience 2013年第1期14卷 1-2页

作者： Philip Tully Henrik Lindén Anders Lansner Matthias H Hennig Department of Computational Biology Royal Institute of Technology (KTH) S-10044 Stockholm Sweden Stockholm Brain Institute Karolinska Institutet 171 77 Stockholm Sweden Institute for Adaptive and Neural Computation University of Edinburgh EH8 9AB Edinburgh UK Department of Numerical Analysis and Computing Science Stockholm University S-10044 Stockholm Sweden

Laplacian preconditioning of elliptic pdes: Localization of the eigenvalues of the discretized operator

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arXiv 2018年

作者： Gergelits, Tomáš Mardal, Kent-André Nielsen, Bjørn Fredrik Strakoš, Zdeněk Institute of Computer Sciences Czech Academy of Science Prague Czech Republic Faculty of Mathematics and Physics Charles University Prague Czech Republic Department of Mathematics University of Oslo Oslo0316 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Lysaker1325 Norway Faculty of Science and Technology Norwegian University of Life Sciences ÅsNO-1432 Norway

In the paper Preconditioning by inverting the Laplacian;an analysis of the eigenvalues. IMA Journal of numerical analysis 29, 1 (2009), 24-42, Nielsen, Hackbusch and Tveito study the operator generated by using the inverse of the Laplacian as preconditioner for second order elliptic PDEs ∇ · (k(x)∇u) = f. They prove that the range of k(x) is contained in the spectrum of the preconditioned operator, provided that k is continuous. Their rigorous analysis only addresses mappings defined on infinite dimensional spaces, but the numerical experiments in the paper suggest that a similar property holds in the discrete case. Motivated by this investigation, we analyze the eigenvalues of the matrix L−1A, where L and A are the stiffness matrices associated with the Laplace operator and general second order elliptic operators, respectively. Without any assumption about the continuity of k(x), we prove the existence of a one-to-one pairing between the eigenvalues of L−1A and the intervals determined by the images under k(x) of the supports of the FE nodal basis functions. As a consequence, we can show that the nodal values of k(x) yield accurate approximations of the eigenvalues of L−1A. Our theoretical results are illuminated by several numerical experiments.65F08, 65F15, 65N12, 35J99 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Consensus-Based Optimization Methods Converge Globally

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arXiv 2021年

作者： Fornasier, Massimo Klock, Timo Riedl, Konstantin Technical University of Munich School of Computation Information and Technology Department of Mathematics Munich Germany Munich Center for Machine Learning Munich Germany Munich Data Science Institute Munich Germany Simula Research Laboratory Department of Numerical Analysis and Scientific Computing Oslo Norway University of San Diego Department of Mathematics San DiegoCA United States

In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that, on average, CBO performs a gradient descent of the squared Euclidean distance to the global minimizer, we devise a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the success of the method. In particular, we prove that CBO performs a convexification of a large class of optimization problems as the number of optimizing agents goes to infinity. Furthermore, we improve prior analyses by requiring mild assumptions about the initialization of the method and by covering objectives that are merely locally Lipschitz continuous. As a core component of this analysis, we establish a quantitative nonasymptotic Laplace principle, which may be of independent interest. From the result of CBO convergence in mean-field law, it becomes apparent that the hardness of any global optimization problem is necessarily encoded in the rate of the mean-field approximation, for which we provide a novel probabilistic quantitative estimate. The combination of these results allows to obtain probabilistic global convergence guarantees of the numerical CBO *** Codes 65K10, 90C26, 90C56, 35Q90, 35Q84 Copyright © 2021, The Authors. All rights reserved.

关键词： Fokker Planck equation

Exploration of core concepts required for mid- and domain-level ontology development to facilitate explainable-AI-readiness of data and models 4

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Exploration of core concepts required for mid- and domain-le...

4th International Workshop on Data meets Ontologies in Explainable AI, DAO-XAI 2024

作者： Horsch, Martin T. Chiacchiera, Silvia Todorov, Ilian T. Correia, Ana Teresa Dey, Aditya Konchakova, Natalia A. Scholze, Sebastian Stephan, Simon Tøndel, Kristin Sarkar, Arkopaul Karray, M. Hedi Al Machot, Fadi Schembera, Björn Norwegian University of Life Sciences Department of Data Science Postboks 5003 Ås1432 Norway UKRI Science and Technology Facilities Council Scientific Computing Department DaresburyWA4 4AD United Kingdom ATB Institut für Angewandte Systemtechnik Bremen GmbH Wiener Str. 1 Bremen28359 Germany Helmholtz-Zentrum Hereon Institute of Surface Science Max-Planck-Str. 1 Geesthacht21502 Germany RPTU Kaiserslautern Laboratory of Engineering Thermodynamics Kaiserslautern67663 Germany University of Technology Tarbes Occitanie Pyrénées Production Engineering Lab. 47 av. d’Azereix Tarbes France University of Stuttgart Institute of Applied Analysis and Numerical Simulation Stuttgart70569 Germany

This position paper reports on the initial discussions within the Knowledge Graph Alliance’s working group on explainable-AI-ready data and metadata principles, which was created in March 2024. At present, we are taking initial steps toward capturing core concepts related to explanation, grounding, reliance, and trust;the scope also extends to potential dual notions such as explainability, verifiability/reproducibility, reliability, and trustworthiness. These initial steps consist in reviewing core concepts as they are discussed in the literature and exploring what could be practically useful definitions of these most central concepts. One of the conclusions is that the metadata standards will need to be suitable for documenting three kinds of grounding: Grounding of knowledge, grounding of reliance, and grounding of trust. Pre-existing metadata standards at the mid and domain level are presently undergoing a redesign in order to become more modular, computationally tractable, intelligible to humans, and adjustable, which will be needed as we continue our work toward actionable recommendations. The development of this system of lite (OWL 2 EL) ontologies, called MSO-EM: Ontologies for modelling, simulation, optimization (MSO) and epistemic metadata (EM), is carried out on a public repository. © 2024 Copyright for this paper by its authors.

关键词： Applied ontology epistemic metadata explainable-AI-ready (XAIR) ontology redesign reliability reproducibility

Application of a dispersive wave hydro-sediment-morphodynamic model in the Ria Formosa lagoon

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arXiv 2022年

作者： Kazhyken, Kazbek Valseth, Eirik Videman, Juha Dawson, Clint Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States CAMGSD Departamento de Matemática Universidade de Lisboa Lisbon1049-001 Portugal Department of Data Science The Norwegian University of Life Sciences Ås1433 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo0164 Norway

Results of an application of a dispersive wave hydro-sediment-morphodynamic model in the western circulation cell of the Ria Formosa lagoon located in the Algarve region of the southern Portugal are presented. This area of interest has a couple of features that complicate the application of the dispersive wave model: (1) the area has a complex irregular geometry with a number of barrier islands that separate the lagoon from the Atlantic Ocean, artificial and naturally occurring tidal inlets, and a number of curling channels inside the lagoon that interconnect the inlets and serve as waterways between the lagoon settlements;(2) the tidal range in the area can reach up to 3.5 m;therefore, the terrain inside the lagoon is characterized by vast salt marshes and tidal flats, and the wetting-drying process is a key component of any hydrodynamic simulation in this area. A model representation of the area has been developed by generating an unstructured finite element mesh of the circulation cell, and collecting data on parameters that characterize the tidal waves in the area, and bottom friction and sediment transport models used in the simulations. The results of the simulations indicate that the dispersive wave model can be applied in coastal areas with nontrivial underlying physical processes, and complex irregular geometries. Moreover, the dispersive term of the model is capable of capturing additional flow characteristics that are otherwise not present in hydrodynamic simulations that involve the nonlinear shallow water equations;and these additional flow features can, in their turn, affect the resulting sediment transport and bed morphodynamic process simulations. Copyright © 2022, The Authors. All rights reserved.

关键词： Equations of motion

A Sensitivity analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks

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arXiv 2024年

作者： Glover, Tom Eivind Jahren, Ruben Martinuzzi, Francesco Lind, Pedro Gonçalves Nichele, Stefano Department of Computer Science OsloMet - Oslo Metropolitan University Oslo Norway Department of Computer Science and Communication Østfold University College Halden Norway Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo0164 Norway Center for Scalable Data Analytics and Artificial Intelligence Leipzig University Leipzig Germany Institute for Earth System Science & Remote Sensing Leipzig University Leipzig Germany Remote Sensing Centre for Earth System Research Leipzig University Leipzig Germany

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself to be difficult, but if combined with reservoir computing (RC), this becomes much more feasible. Furthermore, RC and ECA enable energy-efficient AI, making the combination a promising concept for Edge AI. In this work, we contrast ECA to substrates of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). They are, in comparison, the topological heterogeneous counterparts of ECA. This represents a step from ECA towards more biological-plausible substrates. We analyse these substrates by testing on an RC benchmark (5-bit memory), using Temporal Derrida plots to estimate the sensitivity and assess the defect collapse rate. We find that, counterintuitively, disordered topology does not necessarily mean disordered computation. There are countering computational"forces" of topology imperfections leading to a higher collapse rate (order) and yet, if accounted for, an increased sensitivity to the initial condition. These observations together suggest a shrinking critical range. © 2024, CC BY.

关键词： Sensitivity analysis

Automatic Variationally Stable analysis for Finite Element Computations: Transient Convection-Diffusion Problems

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arXiv 2020年

作者： Valseth, Eirik Behnoudfar, Pouria Dawson, Clint Romkes, Albert Oden Institute for Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway PerthWA6152 Australia Department of Mechanical Engineering South Dakota School of Mines & Technology Rapid CitySD57701 United States

We present an application of stable finite element (FE) approximations of convection-diffusion initial boundary value problems (IBVPs) using a weighted least squares FE method, the automatic variationally stable finite element (AVS-FE) method [1]. The transient convection-diffusion problem leads to issues in classical FE methods as the differential operator can be considered a singular perturbation in both space and time. The stability property of the AVS-FE method, allows us significant flexibility in the construction of FE approximations in both space and time. Thus, in this paper, we take two distinct approaches to the FE discretization of the convection-diffusion problem: i) considering a space-time approach in which the temporal discretization is established using finite elements, and ii) a method of lines approach in which we employ the AVS-FE method in space whereas the temporal domain is discretized using the generalized-α method. We also consider another space-time technique in which the temporal direction is partitioned, thereby leading to finite space-time"slices" in an attempt to reduce the computational cost of the space-time discretizations. We present numerical verifications for these approaches, including numerical asymptotic convergence studies highlighting optimal convergence properties. Furthermore, in the spirit of the discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan [2–6], the AVS-FE method also leads to readily available a posteriori error estimates through a Riesz representer of the residual of the AVS-FE approximations. Hence, the norm of the resulting local restrictions of these estimates serve as error indicators in both space and time for which we present multiple numerical verifications in mesh adaptive *** Codes 65M60 65M12 65M20 65M50 Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method