每年出版 6 期
ISSN 打印: 2152-5080
ISSN 在线: 2152-5099
Indexed in
ADAPTIVE SAMPLING WITH TOPOLOGICAL SCORES
摘要
Understanding and describing expensive black box functions such as physical simulations is a common problem in many application areas. One example is the recent interest in uncertainty quantification with the goal of discovering the relationship between a potentially large number of input parameters and the output of a simulation. Typically, the simulation of interest is expensive to evaluate and thus the sampling of the parameter space is necessarily small. As a result choosing a "good" set of samples at which to evaluate is crucial to glean as much information as possible from the fewest samples. While space-filling sampling designs such as Latin hypercubes provide a good initial cover of the entire domain, more detailed studies typically rely on adaptive sampling: Given an initial set of samples, these techniques construct a surrogate model and use it to evaluate a scoring function which aims to predict the expected gain from evaluating a potential new sample. There exist a large number of different surrogate models as well as different scoring functions each with their own advantages and disadvantages. In this paper we present an extensive comparative study of adaptive sampling using four popular regression models combined with six traditional scoring functions compared against a space-filling design. Furthermore, for a single high-dimensional output function, we introduce a new class of scoring functions based on global topological rather than local geometric information. The new scoring functions are competitive in terms of the root mean squared prediction error but are expected to better recover the global topological structure. Our experiments suggest that the most common point of failure of adaptive sampling schemes are ill-suited regression models. Nevertheless, even given well-fitted surrogate models many scoring functions fail to outperform a space-filling design.
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Salucci Marco, Anselmi Nicola, Oliveri Giacomo, Calmon Pierre, Miorelli Roberto, Reboud Christophe, Massa Andrea, Real-Time NDT-NDE Through an Innovative Adaptive Partial Least Squares SVR Inversion Approach, IEEE Transactions on Geoscience and Remote Sensing, 54, 11, 2016. Crossref
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Beck Joakim, Guillas Serge, Sequential Design with Mutual Information for Computer Experiments (MICE): Emulation of a Tsunami Model, SIAM/ASA Journal on Uncertainty Quantification, 4, 1, 2016. Crossref
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Iuliano Emiliano, Efficient Design Optimization Assisted by Sequential Surrogate Models, International Journal of Aerospace Engineering, 2019, 2019. Crossref
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Salucci Marco, Oliveri Giacomo, Massa Andrea, Real-Time Electrical Impedance Tomography of the Human Chest by Means of a Learning-by-Examples Method, IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology, 3, 2, 2019. Crossref
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Kreitmair Monika Johanna, Introduction and Literature Review, in The Effect of Uncertainty on Tidal Stream Energy Resource Estimates, 2021. Crossref
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Massa Andrea, Salucci Marco, On the Design of Complex EM Devices and Systems Through the System-by-Design Paradigm: A Framework for Dealing With the Computational Complexity, IEEE Transactions on Antennas and Propagation, 70, 2, 2022. Crossref
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Salucci Marco, Oliveri Giacomo, Hannan Mohammad Abdul, Massa Andrea, System-by-Design Paradigm-Based Synthesis of Complex Systems: The case of spline-contoured 3D radomes, IEEE Antennas and Propagation Magazine, 64, 1, 2022. Crossref