Toward real-time optimization through model reduction and model discrepancy sensitivities
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909760244154368 |
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| author | Hart, Joseph McQuarrie, Shane A. Morrow, Zachary Waanders, Bart van Bloemen |
| author_facet | Hart, Joseph McQuarrie, Shane A. Morrow, Zachary Waanders, Bart van Bloemen |
| contents | Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs -- those that do not require access to the full-order model at evaluation time -- is popular because they facilitate optimization solutions can be computed within the wall-clock-time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, $N=\mathcal{O}(1)$ full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution using the full-order model data. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. The HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward real-time optimization through model reduction and model discrepancy sensitivities Hart, Joseph McQuarrie, Shane A. Morrow, Zachary Waanders, Bart van Bloemen Optimization and Control Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs -- those that do not require access to the full-order model at evaluation time -- is popular because they facilitate optimization solutions can be computed within the wall-clock-time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, $N=\mathcal{O}(1)$ full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution using the full-order model data. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. The HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data. |
| title | Toward real-time optimization through model reduction and model discrepancy sensitivities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.21792 |