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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08756 |
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| _version_ | 1866914948720885760 |
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| author | Bubel, Martin Schmid, Jochen Carmesin, Maximilian Kozachynskyi, Volodymyr Esche, Erik Bortz, Michael |
| author_facet | Bubel, Martin Schmid, Jochen Carmesin, Maximilian Kozachynskyi, Volodymyr Esche, Erik Bortz, Michael |
| contents | Calibrating model parameters to measured data by minimizing loss functions is an important step in obtaining realistic predictions from model-based approaches, e.g., for process optimization. This is applicable to both knowledge-driven and data-driven model setups. Due to measurement errors, the calibrated model parameters also carry uncertainty. In this contribution, we use cubature formulas based on sparse grids to calculate the variance of the regression results. The number of cubature points is close to the theoretical minimum required for a given level of exactness. We present exact benchmark results, which we also compare to other cubatures. This scheme is then applied to estimate the prediction uncertainty of the NRTL model, calibrated to observations from different experimental designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cubature-based uncertainty estimation for nonlinear regression models Bubel, Martin Schmid, Jochen Carmesin, Maximilian Kozachynskyi, Volodymyr Esche, Erik Bortz, Michael Methodology Numerical Analysis Calibrating model parameters to measured data by minimizing loss functions is an important step in obtaining realistic predictions from model-based approaches, e.g., for process optimization. This is applicable to both knowledge-driven and data-driven model setups. Due to measurement errors, the calibrated model parameters also carry uncertainty. In this contribution, we use cubature formulas based on sparse grids to calculate the variance of the regression results. The number of cubature points is close to the theoretical minimum required for a given level of exactness. We present exact benchmark results, which we also compare to other cubatures. This scheme is then applied to estimate the prediction uncertainty of the NRTL model, calibrated to observations from different experimental designs. |
| title | Cubature-based uncertainty estimation for nonlinear regression models |
| topic | Methodology Numerical Analysis |
| url | https://arxiv.org/abs/2409.08756 |