Reconstructing Langevin systems from high and low-resolution time series using Euler and Hermite reconstructions Article Swipe
Babak M. S. Arani
,
Stephen R. Carpenter
,
Egbert H. van Nes
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1101/2024.05.30.596585
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1101/2024.05.30.596585
The ecological literature often features phenomenological dynamic models lacking robust validation against observational data. Reverse engineering is an alternative approach, where time series data are utilized to infer or fit a stochastic differential equation. This process, known as system reconstruction, presents significant challenges. This paper addresses the estimation of the (often) non-linear deterministic and stochastic parts of Langevin models, one of the simplest yet commonly used stochastic differential equations. We introduce a Maximum Likelihood Estimation (MLE) inference method, termed Euler reconstruction, tailored for time series data with medium to high resolution. However, the Euler approach is not reliable for low-resolution data. To fill the gap for sparsely sampled data, we present an MLE inference method pioneered by Aït-Sahalia, that we term Hermite reconstruction. We employ a powerful modeling framework utilizing splines to detect inherent nonlinearities in the unknown data-generating system to achieve high accuracy with minimal computational burden. Applying Euler and Hermite reconstructions to a range of simulated, ecological, and climate datasets, we demonstrate their efficacy and versatility. We provide a user-friendly tutorial and a MATLAB package called the ‘MATLAB reconstruction package’.
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- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1101/2024.05.30.596585
- https://www.biorxiv.org/content/biorxiv/early/2024/06/02/2024.05.30.596585.full.pdf
- OA Status
- green
- References
- 21
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399296313
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- OpenAlex ID
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https://openalex.org/W4399296313Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1101/2024.05.30.596585Digital Object Identifier
- Title
-
Reconstructing Langevin systems from high and low-resolution time series using Euler and Hermite reconstructionsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-06-02Full publication date if available
- Authors
-
Babak M. S. Arani, Stephen R. Carpenter, Egbert H. van NesList of authors in order
- Landing page
-
https://doi.org/10.1101/2024.05.30.596585Publisher landing page
- PDF URL
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https://www.biorxiv.org/content/biorxiv/early/2024/06/02/2024.05.30.596585.full.pdfDirect link to full text PDF
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-
YesWhether a free full text is available
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-
greenOpen access status per OpenAlex
- OA URL
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https://www.biorxiv.org/content/biorxiv/early/2024/06/02/2024.05.30.596585.full.pdfDirect OA link when available
- Concepts
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Hermite polynomials, Series (stratigraphy), Euler's formula, Resolution (logic), Statistical physics, Applied mathematics, Mathematics, Algorithm, Physics, Computer science, Mathematical analysis, Geology, Artificial intelligence, PaleontologyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.dynamic | 7 |
| abstract_inverted_index.lacking | 9 |
| abstract_inverted_index.method, | 78 |
| abstract_inverted_index.minimal | 146 |
| abstract_inverted_index.models, | 59 |
| abstract_inverted_index.package | 177 |
| abstract_inverted_index.present | 111 |
| abstract_inverted_index.provide | 170 |
| abstract_inverted_index.sampled | 108 |
| abstract_inverted_index.splines | 131 |
| abstract_inverted_index.unknown | 138 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.Applying | 149 |
| abstract_inverted_index.However, | 92 |
| abstract_inverted_index.Langevin | 58 |
| abstract_inverted_index.accuracy | 144 |
| abstract_inverted_index.approach | 95 |
| abstract_inverted_index.commonly | 65 |
| abstract_inverted_index.efficacy | 166 |
| abstract_inverted_index.features | 5 |
| abstract_inverted_index.inherent | 134 |
| abstract_inverted_index.modeling | 128 |
| abstract_inverted_index.powerful | 127 |
| abstract_inverted_index.presents | 41 |
| abstract_inverted_index.process, | 36 |
| abstract_inverted_index.reliable | 98 |
| abstract_inverted_index.simplest | 63 |
| abstract_inverted_index.sparsely | 107 |
| abstract_inverted_index.tailored | 82 |
| abstract_inverted_index.tutorial | 173 |
| abstract_inverted_index.utilized | 26 |
| abstract_inverted_index.addresses | 46 |
| abstract_inverted_index.approach, | 20 |
| abstract_inverted_index.datasets, | 162 |
| abstract_inverted_index.equation. | 34 |
| abstract_inverted_index.framework | 129 |
| abstract_inverted_index.inference | 77, 114 |
| abstract_inverted_index.introduce | 71 |
| abstract_inverted_index.pioneered | 116 |
| abstract_inverted_index.utilizing | 130 |
| abstract_inverted_index.‘MATLAB | 180 |
| abstract_inverted_index.Estimation | 75 |
| abstract_inverted_index.Likelihood | 74 |
| abstract_inverted_index.ecological | 2 |
| abstract_inverted_index.equations. | 69 |
| abstract_inverted_index.estimation | 48 |
| abstract_inverted_index.literature | 3 |
| abstract_inverted_index.non-linear | 52 |
| abstract_inverted_index.simulated, | 158 |
| abstract_inverted_index.stochastic | 32, 55, 67 |
| abstract_inverted_index.validation | 11 |
| abstract_inverted_index.alternative | 19 |
| abstract_inverted_index.challenges. | 43 |
| abstract_inverted_index.demonstrate | 164 |
| abstract_inverted_index.ecological, | 159 |
| abstract_inverted_index.engineering | 16 |
| abstract_inverted_index.package’. | 182 |
| abstract_inverted_index.resolution. | 91 |
| abstract_inverted_index.significant | 42 |
| abstract_inverted_index.differential | 33, 68 |
| abstract_inverted_index.versatility. | 168 |
| abstract_inverted_index.Aït-Sahalia, | 118 |
| abstract_inverted_index.computational | 147 |
| abstract_inverted_index.deterministic | 53 |
| abstract_inverted_index.observational | 13 |
| abstract_inverted_index.user-friendly | 172 |
| abstract_inverted_index.low-resolution | 100 |
| abstract_inverted_index.nonlinearities | 135 |
| abstract_inverted_index.reconstruction | 181 |
| abstract_inverted_index.data-generating | 139 |
| abstract_inverted_index.reconstruction, | 40, 81 |
| abstract_inverted_index.reconstruction. | 123 |
| abstract_inverted_index.reconstructions | 153 |
| abstract_inverted_index.phenomenological | 6 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5103109898 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I169381384 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/13 |
| sustainable_development_goals[0].score | 0.8399999737739563 |
| sustainable_development_goals[0].display_name | Climate action |
| citation_normalized_percentile.value | 0.09944308 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |