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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.12011 |
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| _version_ | 1866910472139177984 |
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| author | Williams, Jan P. Zahn, Olivia Kutz, J. Nathan |
| author_facet | Williams, Jan P. Zahn, Olivia Kutz, J. Nathan |
| contents | Sensing is a universal task in science and engineering. Downstream tasks from sensing include inferring full state estimates of a system (system identification), control decisions, and forecasting. These tasks are exceptionally challenging to achieve with limited sensors, noisy measurements, and corrupt or missing data. We propose a SHallow REcurrent Decoder (SHRED) neural network structure for sensing which incorporates (i) a recurrent neural network (LSTM) to learn a latent representation of the temporal dynamics of the sensors, and (ii) a shallow decoder that learns a mapping between this latent representation and the high-dimensional state space. By explicitly accounting for the time-history, or trajectory, of the sensor measurements, SHRED enables accurate reconstructions with far fewer sensors, outperforms existing techniques when more measurements are available, and is agnostic towards sensor placement. In addition, a compressed representation of the high-dimensional state is directly obtained from sensor measurements, which provides an on-the-fly compression for modeling physical and engineering systems. Forecasting is also achieved from the sensor time-series data alone, producing an efficient paradigm for predicting temporal evolution with an exceptionally limited number of sensors. In the example cases explored, including turbulent flows, complex spatio-temporal dynamics can be characterized with exceedingly limited sensors that can be randomly placed with minimal loss of performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sensing with shallow recurrent decoder networks Williams, Jan P. Zahn, Olivia Kutz, J. Nathan Dynamical Systems Sensing is a universal task in science and engineering. Downstream tasks from sensing include inferring full state estimates of a system (system identification), control decisions, and forecasting. These tasks are exceptionally challenging to achieve with limited sensors, noisy measurements, and corrupt or missing data. We propose a SHallow REcurrent Decoder (SHRED) neural network structure for sensing which incorporates (i) a recurrent neural network (LSTM) to learn a latent representation of the temporal dynamics of the sensors, and (ii) a shallow decoder that learns a mapping between this latent representation and the high-dimensional state space. By explicitly accounting for the time-history, or trajectory, of the sensor measurements, SHRED enables accurate reconstructions with far fewer sensors, outperforms existing techniques when more measurements are available, and is agnostic towards sensor placement. In addition, a compressed representation of the high-dimensional state is directly obtained from sensor measurements, which provides an on-the-fly compression for modeling physical and engineering systems. Forecasting is also achieved from the sensor time-series data alone, producing an efficient paradigm for predicting temporal evolution with an exceptionally limited number of sensors. In the example cases explored, including turbulent flows, complex spatio-temporal dynamics can be characterized with exceedingly limited sensors that can be randomly placed with minimal loss of performance. |
| title | Sensing with shallow recurrent decoder networks |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2301.12011 |