Identification of Partial-Differential-Equations-Based Models from Noisy Data via Splines
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916950193471488 |
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| author | Zhao, Yujie Huo, Xiaoming Mei, Yajun |
| author_facet | Zhao, Yujie Huo, Xiaoming Mei, Yajun |
| contents | We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the cubic splines to estimate unobservable derivatives. The underlying PDE is based on a subset of these derivatives. This stage is computationally efficient: its computational complexity is a product of a constant with the sample size; this is the lowest possible order of computational complexity. In the second stage, we apply the Least Absolute Shrinkage and Selection Operator (Lasso) to identify the underlying PDE-based model. Statistical properties are developed, including the model identification accuracy. We validate our theory through various numerical examples and a real data case study. The case study is based on a National Aeronautics and Space Administration (NASA) data set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_10231 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Identification of Partial-Differential-Equations-Based Models from Noisy Data via Splines Zhao, Yujie Huo, Xiaoming Mei, Yajun Methodology We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the cubic splines to estimate unobservable derivatives. The underlying PDE is based on a subset of these derivatives. This stage is computationally efficient: its computational complexity is a product of a constant with the sample size; this is the lowest possible order of computational complexity. In the second stage, we apply the Least Absolute Shrinkage and Selection Operator (Lasso) to identify the underlying PDE-based model. Statistical properties are developed, including the model identification accuracy. We validate our theory through various numerical examples and a real data case study. The case study is based on a National Aeronautics and Space Administration (NASA) data set. |
| title | Identification of Partial-Differential-Equations-Based Models from Noisy Data via Splines |
| topic | Methodology |
| url | https://arxiv.org/abs/2103.10231 |