Inference in Latent Force Models Using Optimal State Estimation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915692584894464 |
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| author | Wolff, Tobias M. Lopez, Victor G. Müller, Matthias A. Beckers, Thomas |
| author_facet | Wolff, Tobias M. Lopez, Victor G. Müller, Matthias A. Beckers, Thomas |
| contents | Latent force models, a class of hybrid modeling approaches, integrate physical knowledge of system dynamics with a latent force - an unknown, unmeasurable input modeled as a Gaussian process. In this work, we introduce two optimal state estimation frameworks to reconstruct the latent forces and to estimate the states. In contrast to state-of-the-art approaches, the designed estimators enable the consideration of system-inherent constraints. Finally, the performance of the novel frameworks is investigated in several numerical examples. In particular, we demonstrate the performance of the new framework in a real-world biomedical example - the hypothalamic-pituitary-thyroid axis - using hormone measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inference in Latent Force Models Using Optimal State Estimation Wolff, Tobias M. Lopez, Victor G. Müller, Matthias A. Beckers, Thomas Systems and Control Latent force models, a class of hybrid modeling approaches, integrate physical knowledge of system dynamics with a latent force - an unknown, unmeasurable input modeled as a Gaussian process. In this work, we introduce two optimal state estimation frameworks to reconstruct the latent forces and to estimate the states. In contrast to state-of-the-art approaches, the designed estimators enable the consideration of system-inherent constraints. Finally, the performance of the novel frameworks is investigated in several numerical examples. In particular, we demonstrate the performance of the new framework in a real-world biomedical example - the hypothalamic-pituitary-thyroid axis - using hormone measurements. |
| title | Inference in Latent Force Models Using Optimal State Estimation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.20250 |