Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning
© 2020 authors. Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and...
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| Format: | Article |
| Language: | English |
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American Physical Society (APS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/134435 |
| _version_ | 1826213765465505792 |
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| author | Lu, Peter Y Kim, Samuel Soljačić, Marin |
| author_facet | Lu, Peter Y Kim, Samuel Soljačić, Marin |
| author_sort | Lu, Peter Y |
| collection | MIT |
| description | © 2020 authors. Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with R2>0.95) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle. |
| first_indexed | 2024-09-23T15:54:28Z |
| format | Article |
| id | mit-1721.1/134435 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:54:28Z |
| publishDate | 2021 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1344352021-10-28T03:16:58Z Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning Lu, Peter Y Kim, Samuel Soljačić, Marin © 2020 authors. Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with R2>0.95) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle. 2021-10-27T20:05:00Z 2021-10-27T20:05:00Z 2020 2021-07-09T12:17:44Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134435 en 10.1103/PHYSREVX.10.031056 Physical Review X Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf American Physical Society (APS) APS |
| spellingShingle | Lu, Peter Y Kim, Samuel Soljačić, Marin Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title | Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title_full | Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title_fullStr | Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title_full_unstemmed | Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title_short | Extracting Interpretable Physical Parameters from Spatiotemporal Systems Using Unsupervised Learning |
| title_sort | extracting interpretable physical parameters from spatiotemporal systems using unsupervised learning |
| url | https://hdl.handle.net/1721.1/134435 |
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