2063 research outputs found
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EDA++: Estimation of Distribution Algorithms with Feasibility Conserving Mechanisms for Constrained Continuous Optimization
Get PDFHandling non-linear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and non-linear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this paper, we adopt the framework of Estimation of Distribution Algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with non-linear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint handling methods. Conducted experiments confirm the speed, robustness and efficiency of the proposed algorithm in tackling various problems with linear and non-linear constraints.La Caixa Foundatio
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
Get PDFIn this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the interface are sufficiently smooth, the depth cannot vanish in finite time. This results holds regardless of gravity and surface tension effects or, if applicable, the stratification in multiphase flows
Machine learning from crowds using candidate set-based labelling
Get PDFCrowdsourcing is a popular cheap alternative in machine learning for gathering information from a set of annotators. Learning from crowd-labelled data involves dealing with its inherent uncertainty and inconsistencies. In the classical framework, each annotator provides a single label per example, which fails to capture the complete knowledge of annotators. We propose candidate labelling, that is, to allow annotators to provide a set of candidate labels for each example and thus express their doubts. We propose an appropriate model for the annotators, and present two novel learning methods that deal with the two basic steps (label aggregation and model learning) sequentially or jointly. Our empirical study shows the advantage of candidate labelling and the proposed methods with respect to the classical framework
On the relative value of weak information of supervision for learning generative models: An empirical study
Get PDFWeakly supervised learning is aimed to learn predictive models from partially supervised data, an easy-to-collect alternative to the costly standard full supervision. During the last decade, the research community has striven to show that learning reliable models in specific weakly supervised problems is possible. We present an empirical study that analyzes the value of weak information of supervision throughout its entire spectrum, from none to full supervision. Its contribution is assessed under the realistic assumption that a small subset of fully supervised data is available. Particularized in the problem of learning with candidate sets, we adapt Cozman and Cohen [1] key study to learning from weakly supervised data. Standard learning techniques are used to infer generative models from this type of supervision with both synthetic and real data. Empirical results suggest that weakly labeled data is helpful in realistic scenarios, where fully labeled data is scarce, and its contribution is directly related to both the amount of information of supervision and how meaningful this information is
LASSO for streaming data with adaptative filtering
Get PDFStreaming data is ubiquitous in modern machine learning, and so the development of scalable algorithms to analyze this sort of information is a topic of current interest. On the other hand, the problem of l1-penalized least-square regression, commonly referred to as LASSO, is a quite popular data mining technique, which is commonly used for feature selection. In this work, we develop a homotopy-based solver for LASSO, on a streaming data context, that massively speeds up its convergence by extracting the most information out of the solution prior to receiving the latest batch of data. Since these batches may show a non-stationary behavior, our solver also includes an adaptive filter that improves the predictability of our method in this scenario. Besides different theoretical properties, we additionally compare empirically our solver to the state-of-the-art: LARS, coordinate descent and Garrigues and Ghaoui’s data streaming homotopy. The obtained results show our approach to massively reduce the computational time require to convergence for the previous approaches, reducing up to 3, 4 and 5 orders of magnitude of running time with respect to LARS, coordinate descent and Garrigues and Ghaoui’s homotopy, respectively
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
Get PDFWe revisit a result from “Pointwise convergence of the Schr ̈odinger
flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research
Notices, 2021 (1), 596-647” regarding the pointwise convergence of solutions
to the periodic cubic nonlinear Schr ̈odinger equation in dimension d = 2
PyDDRBG: A Python framework for benchmarking and evaluating static and dynamic multimodal optimization methods
Get PDFPyDDRBG is a Python framework for generating tunable test problems for static and dynamic multimodal optimization. It allows for quick and simple generation of a set of predefined problems for non-experienced users, as well as highly customized problems for more experienced users. It easily integrates with an arbitrary optimization method. It can calculate the optimization performance when measured according to the robust mean peak ratio. PyDDRBG is expected to advance the fields of static and dynamic multimodal optimization by providing a common platform to facilitate the numerical analysis, evaluation, and comparison in these fields
Curve-guided 5-axis CNC flank milling of free-form surfaces using custom-shaped tools
Get PDFA new method for 5-axis flank milling of free-form surfaces is proposed. Existing flank milling path-planning methods typically use on-market milling tools whose shape is cylindrical or conical, and is therefore not well-suited for meeting fine tolerances for manufacturing of benchmark free-form surfaces like turbine blades, gears, or blisks. In contrast, our optimization-based framework incorporates the shape of the tool into the optimization cycle and looks not only for the milling paths, but also for the shape of the tool itself. Given a free-form reference surface and a guiding path that roughly indicates the motion of the milling tool, tangential movability of quadruplets of spheres centered along a straight line is analyzed to indicate possible shapes and their motions. This results in Hermite data in the space of rigid body motions that are interpolated and further optimized, both in terms of the motion and the shape of the milling tool itself. We demonstrate our algorithm on synthetic free-form surfaces and industrial benchmark datasets, showing that the use of custom-shaped tools is capable of meeting fine industrial tolerances and outperforms the use of classical, on-market tools.RYC-2017-2264
Analysis of Dominant Classes in Universal Adversarial Perturbations
Get PDFThe reasons why Deep Neural Networks are susceptible to being fooled by adversarial examples remains an open discussion. Indeed, many differ- ent strategies can be employed to efficiently generate adversarial attacks, some of them relying on different theoretical justifications. Among these strategies, universal (input-agnostic) perturbations are of particular inter- est, due to their capability to fool a network independently of the input in which the perturbation is applied. In this work, we investigate an in- triguing phenomenon of universal perturbations, which has been reported previously in the literature, yet without a proven justification: universal perturbations change the predicted classes for most inputs into one par- ticular (dominant) class, even if this behavior is not specified during the creation of the perturbation. In order to justify the cause of this phe- nomenon, we propose a number of hypotheses and experimentally test them using a speech command classification problem in the audio domain as a testbed. Our analyses reveal interesting properties of universal per- turbations, suggest new methods to generate such attacks and provide an explanation of dominant classes, under both a geometric and a data- feature perspective.IT1244-19
PRE_2019_1_0128
TIN2016-78365-R
PID2019-104966GB-I00
FPU19/0323
An implicit symplectic solver for high-precision long term integrations of the Solar System
Get PDFWe present FCIRK16, a 16th-order implicit symplectic integrator for long-term high precision Solar System simulations. Our integrator takes advantage of the near-Keplerian motion of the planets around the Sun by alternating Keplerian motions with corrections accounting for the planetary interactions. Compared to other symplectic integrators (the Wisdom and Holman map and its higher order generalizations) that also take advantage of the hierarchical nature of the motion of the planets around the central star, our methods require solving implicit equations at each time-step. We claim that, despite this disadvantage, FCIRK16 is more efficient than explicit symplectic integrators for high precision simulations thanks to: (i) its high order of precision, (ii) its easy parallelization, and (iii) its efficient mixed-precision implementation which reduces the effect of round-off errors. In addition, unlike typical explicit symplectic integrators for near Keplerian problems, FCIRK16 is able to integrate problems with arbitrary perturbations (non necessarily split as a sum of integrable parts).
We present a novel analysis of the effect of close encounters in the leading term of the local discretization errors of our integrator. Based on that analysis, a mechanism to detect and refine integration steps that involve close encounters is incorporated in our code. That mechanism allows FCIRK16 to accurately resolve close encounters of arbitrary bodies. We illustrate our treatment of close encounters with the application of FCIRK16 to a point mass Newtonian 15-body model of the Solar System (with the Sun, the eight planets, Pluto, and five main asteroids) and a 16-body model treating the Moon as a separate body. We also present some numerical comparisons of FCIRK16 with a state-of-the-art high order explicit symplectic scheme for 16-body model that demonstrate the superiority of our integrator when very high precision is required.Consolidated Research Group MATHMODE (IT1294-19