Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10920 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911379094503424 |
|---|---|
| author | Bukshtynov, Vladislav |
| author_facet | Bukshtynov, Vladislav |
| contents | State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics, engineering, and materials science. This review surveys PDE-constrained optimization approaches for such inverse problems, emphasizing the underlying mathematical theory and key computational advances developed since 2011. We discuss variational formulations, adjoint-based gradient methods, regularization strategies, and modern computational frameworks, and highlight representative applications, with particular emphasis on identifiability, ill-posedness, and structural limits of state-dependent inverse problems. The review concludes with major open challenges and emerging research directions related to nonconvexity, identifiability, regularization, adjoint computation, data limitations, and model-class dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10920 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variational State-Dependent Inverse Problems in PDE-Constrained Optimization: A Survey of Contemporary Computational Methods and Applications Bukshtynov, Vladislav Optimization and Control State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics, engineering, and materials science. This review surveys PDE-constrained optimization approaches for such inverse problems, emphasizing the underlying mathematical theory and key computational advances developed since 2011. We discuss variational formulations, adjoint-based gradient methods, regularization strategies, and modern computational frameworks, and highlight representative applications, with particular emphasis on identifiability, ill-posedness, and structural limits of state-dependent inverse problems. The review concludes with major open challenges and emerging research directions related to nonconvexity, identifiability, regularization, adjoint computation, data limitations, and model-class dependence. |
| title | Variational State-Dependent Inverse Problems in PDE-Constrained Optimization: A Survey of Contemporary Computational Methods and Applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.10920 |