2063 research outputs found
Sort by
Geometric Hermite interpolation by rational curves of constant width
Get PDFA constructive characterization of the support function for a rationally parameterized curve of constant width is given. In addition, a Hermite interpolation problem for such kind of curves is solved, which yields a method to determine a rational curve of constant width that passes through a set of free points with the corresponding tangent directions. Finally, the case of piecewise rational support functions is considered, which increases the design freedom. The procedure is presented in the general case of hedgehogs of constant width taking the advantage of projective hedgehogs, so that some constraints must be taken to ensure convexity of the desired curve.Funding for the other authors not affiliated with BCAM:
Grant PID2021-124577NBI00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”.
Project PID2019-104927GB-C21 funded by MCIN/AEI/10.13039/501100011033.
Project UJI-B2022-19 funded by Universitat Jaume I.
Project CIAICO/2021/180 funded by Generalitat Valenciana
New Knowledge about the Elementary Landscape Decomposition for Solving the Quadratic Assignment Problem
Get PDFPrevious works have shown that studying the characteristics of the Quadratic Assignment Problem (QAP) is a crucial step in gaining knowledge that can be used to design tailored meta-heuristic algorithms. One way to analyze the characteristics of the QAP is to decompose its objective function into a linear combination of orthogonal sub-functions that can be independently studied. In particular, this work focuses on a decomposition approach that has attracted considerable attention: The Elementary Landscape Decomposition (ELD).The main drawback of the ELD is that it does not allow an understandable characterization of what is being measured by each component of the decomposition. Thus, it turns out difficult to design new efficient meta-heuristic algorithms for the QAP based on the ELD. To address this issue, in this work, we delve deeper into the ELD by means of an additional decomposition of its elementary components. Conducted experiments show that the performed analysis may be used to explain the behaviour of ELD-based methods, providing critical information about their potential applications
Efficient Learning of Minimax Risk Classifiers in High Dimensions
Get PDFHigh-dimensional data is common in multiple areas, such as health care and genomics, where the
number of features can be tens of thousands. In
such scenarios, the large number of features often leads to inefficient learning. Constraint generation methods have recently enabled efficient learning of L1-regularized support vector machines
(SVMs). In this paper, we leverage such methods
to obtain an efficient learning algorithm for the recently proposed minimax risk classifiers (MRCs).
The proposed iterative algorithm also provides a
sequence of worst-case error probabilities and performs feature selection. Experiments on multiple
high-dimensional datasets show that the proposed
algorithm is efficient in high-dimensional scenarios. In addition, the worst-case error probability
provides useful information about the classifier
performance, and the features selected by the algorithm are competitive with the state-of-the-art.CNS2022-13520
Memory-Based Monte Carlo Integration for Solving Partial Differential Equations Using Neural Networks
Get PDFMonte Carlo integration is a widely used quadrature rule to solve Partial Differential Equations with neural networks due to its ability to guarantee overfitting-free solutions and high-dimensional scalability. However, this stochastic method produces noisy losses and gradients during training, which hinders a proper convergence diagnosis. Typically, this is overcome using an immense (disproportionate) amount of integration points, which deteriorates the training performance. This work proposes a memory-based Monte Carlo integration method that produces accurate integral approximations without requiring the high computational costs of processing large samples during training
Swimming Efficiently by Wrapping
Get PDFSingle flagellated bacteria are ubiquitous in nature. They exhibit various swimming
modes using their flagella to explore complex surroundings such as soil and porous
polymer networks. Some single-flagellated bacteria swim with two distinct modes, one
with its flagellum extended away from its body and another with its flagellum wrapped
around it. The wrapped mode has been observed when the bacteria swim under tight
confinements or in highly viscous polymeric melts. In this study we investigate the
hydrodynamics of these two modes inside a circular pipe. We find that the wrap mode is
slower than the extended mode in bulk but more efficient under strong confinement due
to a hydrodynamic increased of its flagellum translation-rotation coupling
Boundedness properties of maximal operators on Lorentz spaces
Get PDFWe study mapping properties of the centered Hardy--Littlewood maximal operator acting on Lorentz spaces. Given and a metric measure space we let be the set of all pairs such that is bounded from to . Under mild assumptions on , for each fixed all possible shapes of are characterized. Namely, we show that the boundary of either is empty or takes the form
, where and is concave, nondecreasing, and satisfies . Conversely, for each such we find such that is bounded from to if and only if the point lies on or under the graph of , that is, and .National Science Centre of Poland (2016/21/N/ST1/01496),
Basque Government (BERC 2022-2025),
Spanish State Research Agency (CEX2021-001142-S and RYC2021-031981-I),
Foundation for Polish Science (START 032.2022)
Multimodal variational autoencoder for inverse problems in geophysics: application to a 1-D magnetotelluric problem
Get PDFEstimating subsurface properties from geophysical measurements is a common inverse problem. Several Bayesian methods currently aim to find the solution to a geophysical inverse problem and quantify its uncertainty. However, most geophysical applications exhibit more than one plausible solution. Here, we propose a multimodal variational autoencoder model that employs a mixture of truncated Gaussian densities to provide multiple solutions, along with their probability of occurrence and a quantification of their uncertainty. This autoencoder is assembled with an encoder and a decoder, where the first one provides a mixture of truncated Gaussian densities from a neural network, and the second is the numerical solution of the forward problem given by the geophysical approach. The proposed method is illustrated with a 1-D magnetotelluric inverse problem and recovers multiple plausible solutions with different uncertainty quantification maps and probabilities that are in agreement with known physical observations.PDC2021-121093-I00
IA4TE
Time-Varying Lyapunov Control Laws with Enhanced Estimation of Distribution Algorithm for Low-Thrust Trajectory Design
Get PDFEnhancements in evolutionary optimization techniques are rapidly growing in many aspects of engineering, specifically in astrodynamics and space trajectory optimization and design. In this chapter, the problem of optimal design of space trajectories is tackled via an enhanced optimization algorithm within the framework of Estimation of Distribution Algorithms (EDAs), incorporated with Lyapunov and Q-law feedback control methods. First, both a simple Lyapunov function and a Q-law are formulated in Classical Orbital Elements (COEs) to provide a closed-loop low-thrust trajectory profile. The weighting coefficients of these controllers are approximated with various degrees of Hermite interpolation splines. Following this model, the unknown time series of weighting coefficients are converted to unknown interpolation points. Considering the interpolation points as the decision variables, a black-box optimization problem is formed with transfer time and fuel mass as the objective functions. An enhanced EDA is proposed and utilized to find the optimal variation of weighting coefficients for minimum-time and minimum-fuel transfer trajectories. The proposed approach is applied in some trajectory optimization problems of Earth-orbiting satellites. Results show the efficiency and the effectiveness of the proposed approach in finding optimal transfer trajectories. A comparison between the Q-law and simple Lyapunov controller is done to show the potential of the potential of the EEDA in enabling the simple Lyapunov controller to recover the finer nuances explicitly given within the analytical expressions in the Q-law
On building physics-based AI models for the design and SHM of mooring systems
Get PDFExpert systems in industrial processes are modelled using physics-based approaches, data-driven models or hybrid approaches in which however the underlying physical models generally constitute a separate block with respect to the Artificial Intelligence (AI) technique(s). This work applies the novel concept of “imbrication”-a physics-based AI approach-to the mooring system of offshore renewable energy devices to achieve a complete integration of both perspectives. This approach can reduce the size of the training dataset and computational time while delivering algorithms with higher generalization capability and explicability. We first undertake the design of the mooring system by developing a surrogate model coupled with a Bayesian optimiser. Then, we analyse the structural health monitoring of the mooring system by designing a supervised Deep Neural Network architecture. Herein, we describe the characteristics of the imbrication process, analyse preliminary results of our investigation and provide considerations for orienting further research work and sector applicability