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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03240 |
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| _version_ | 1866918011252768768 |
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| author | Hu, Yuzhong Kang, Jiayi Ma, Lei Zhang, Xiaoming |
| author_facet | Hu, Yuzhong Kang, Jiayi Ma, Lei Zhang, Xiaoming |
| contents | Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward Kolmogorov Equation (FKE). Previous researches have shown that the method can be applied to highly nonlinear and high dimensional problems. However, when time-varying coefficients are involved in the system models, developing an implementation of the method with high computational speed and low data storage still presents a challenge. To address these limitations, this paper proposes a novel numerical algorithm that incorporates physics-informed neural network (PINN) and principal component analysis (PCA) to solve the FKE approximately. Equipped with this algorithm, the Yau-Yau filter can be implemented by an offline stage for the training of a solver for the approximate solution of FKE and an online stage for its execution. Results of three examples indicate that this implementation is accurate, both time-efficient and storage-efficient for online computation, and is superior than existing nonlinear filtering methods such as extended Kalman filter and particle filter. It is capable of applications to practical nonlinear time-variant filtering problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A novel implementation of Yau-Yau filter for time-variant nonlinear problems Hu, Yuzhong Kang, Jiayi Ma, Lei Zhang, Xiaoming Optimization and Control Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward Kolmogorov Equation (FKE). Previous researches have shown that the method can be applied to highly nonlinear and high dimensional problems. However, when time-varying coefficients are involved in the system models, developing an implementation of the method with high computational speed and low data storage still presents a challenge. To address these limitations, this paper proposes a novel numerical algorithm that incorporates physics-informed neural network (PINN) and principal component analysis (PCA) to solve the FKE approximately. Equipped with this algorithm, the Yau-Yau filter can be implemented by an offline stage for the training of a solver for the approximate solution of FKE and an online stage for its execution. Results of three examples indicate that this implementation is accurate, both time-efficient and storage-efficient for online computation, and is superior than existing nonlinear filtering methods such as extended Kalman filter and particle filter. It is capable of applications to practical nonlinear time-variant filtering problems. |
| title | A novel implementation of Yau-Yau filter for time-variant nonlinear problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.03240 |