{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T02:31:18Z","timestamp":1787797878460,"version":"build-2784847793"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004955","name":"FFG","doi-asserted-by":"publisher","award":["877158"],"award-info":[{"award-number":["877158"]}],"id":[{"id":"10.13039\/501100004955","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004955","name":"FFG","doi-asserted-by":"publisher","award":["01112018"],"award-info":[{"award-number":["01112018"]}],"id":[{"id":"10.13039\/501100004955","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The Federal State of Lower Austria","award":["877158"],"award-info":[{"award-number":["877158"]}]},{"name":"The Federal State of Lower Austria","award":["01112018"],"award-info":[{"award-number":["01112018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens\u2019 theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically-interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and compared to a cubic spline interpolation and a linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches. Further, the results suggest that the variance of second derivatives along a given phase space trajectory is a valuable tool for phase space analysis of non-model time series data, and we expect it to be useful for future research.<\/jats:p>","DOI":"10.3390\/e24050718","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T03:20:43Z","timestamp":1652844043000},"page":"718","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Interpolating Strange Attractors via Fractional Brownian Bridges"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2206-9263","authenticated-orcid":false,"given":"Sebastian","family":"Raubitzek","sequence":"first","affiliation":[{"name":"TU Wien, Information and Software Engineering Group, Favoritenstrasse 9-11\/194, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9814-6045","authenticated-orcid":false,"given":"Thomas","family":"Neubauer","sequence":"additional","affiliation":[{"name":"TU Wien, Information and Software Engineering Group, Favoritenstrasse 9-11\/194, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9862-6268","authenticated-orcid":false,"given":"Jan","family":"Friedrich","sequence":"additional","affiliation":[{"name":"ForWind, Institute of Physics, University of Oldenburg, K\u00fcpkersweg 70, 26129 Oldenburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9272-6225","authenticated-orcid":false,"given":"Andreas","family":"Rauber","sequence":"additional","affiliation":[{"name":"TU Wien, Information and Software Engineering Group, Favoritenstrasse 9-11\/194, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"L71","DOI":"10.1086\/587957","article-title":"Heating the Solar Wind by a Magnetohydrodynamic Turbulent Energy Cascade","volume":"677","author":"Marino","year":"2008","journal-title":"Astrophys. 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