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Reconstructing Piezoelectric Responses over a Lattice: Adaptive Sampling of Low Dimensional Time Series Representations Based on Relative Isolation and Gradient Size

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Part of the Communications in Computer and Information Science book series (CCIS,volume 1512)


We consider a \(d-\)dimensional lattice of points where, at each lattice point, a time series can be measured. We are interested in reconstructing the time series at all points of the lattice, to a desired error tolerance, by adaptively sampling only a subset of lattice points, each over a potentially short time interval. The method we develop is tailored to atomic force microscopy (AFM) data where time series are well-represented by constant functions at each lattice point. Through a convex weighting of a point’s relative isolation and relative gradient size, we assign a sampling priority. Our method adaptively samples the time series and then reconstructs the time series over the entire lattice. Our adaptive sampling scheme performs significantly better than sampling points homogeneously. We find that for the data provided, we can capture piezoelectric relaxation dynamics and achieve a relative \(\ell _2\) reconstruction error of less than \(10\%\) with a \(47\%\) reduction in measurements, and less than \(5\%\) with a \(25\%\) reduction in measurements.

M. R. Lindstrom and W. J. Swartworth—Equal contributions.

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WJS and DN acknowledge funding from NSF BIGDATA #1740325 and NSF DMS #2011140.

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Correspondence to Michael R. Lindstrom or William J. Swartworth .

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Lindstrom, M.R., Swartworth, W.J., Needell, D. (2022). Reconstructing Piezoelectric Responses over a Lattice: Adaptive Sampling of Low Dimensional Time Series Representations Based on Relative Isolation and Gradient Size. In: Nichols, J., et al. Driving Scientific and Engineering Discoveries Through the Integration of Experiment, Big Data, and Modeling and Simulation. SMC 2021. Communications in Computer and Information Science, vol 1512. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96497-9

  • Online ISBN: 978-3-030-96498-6

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