Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
- We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework, a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens's embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.
| Author details: | Georg A. GottwaldORCiDGND, Sebastian ReichORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1063/5.0066080 |
| ISSN: | 1054-1500 |
| ISSN: | 1089-7682 |
| Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/34717332 |
| Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
| Publisher: | AIP |
| Place of publishing: | Melville |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/10/12 |
| Publication year: | 2021 |
| Release date: | 2023/06/22 |
| Volume: | 31 |
| Issue: | 10 |
| Article number: | 101103 |
| Number of pages: | 8 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [318763901-SFB1294] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
