A Gauss-Newton Method with No Additional PDE Solves Beyond Gradient Evaluation for Large-Scale PDE-Constrained Inverse Problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914377665347584 |
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| author | Cherry, Cash Fung, Samy Wu Tenorio, Luis Bozdağ, Ebru |
| author_facet | Cherry, Cash Fung, Samy Wu Tenorio, Luis Bozdağ, Ebru |
| contents | Partial Differential Equation (PDE)-constrained optimization problems often take the form of an optimization of an objective function given as a sum of loss terms. Each function or gradient evaluation requires one or more PDE solves, which render these problems computationally demanding. While Gauss-Newton methods are well-suited for large-scale PDE-constrained optimization, their application to settings such as Full-Waveform Inversion (FWI) is hindered by the need for additional PDE solves to compute Jacobian-vector products. This paper proposes a Gauss-Newton approach that eliminates the need for extra PDE solves beyond those required for gradient computation. Our numerical experiments on FWI demonstrate that the proposed method achieves the efficiency of gradient-based schemes while retaining the fast convergence of Gauss-Newton methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Gauss-Newton Method with No Additional PDE Solves Beyond Gradient Evaluation for Large-Scale PDE-Constrained Inverse Problems Cherry, Cash Fung, Samy Wu Tenorio, Luis Bozdağ, Ebru Optimization and Control Numerical Analysis 65K10, 86A15, 86A22 Partial Differential Equation (PDE)-constrained optimization problems often take the form of an optimization of an objective function given as a sum of loss terms. Each function or gradient evaluation requires one or more PDE solves, which render these problems computationally demanding. While Gauss-Newton methods are well-suited for large-scale PDE-constrained optimization, their application to settings such as Full-Waveform Inversion (FWI) is hindered by the need for additional PDE solves to compute Jacobian-vector products. This paper proposes a Gauss-Newton approach that eliminates the need for extra PDE solves beyond those required for gradient computation. Our numerical experiments on FWI demonstrate that the proposed method achieves the efficiency of gradient-based schemes while retaining the fast convergence of Gauss-Newton methods. |
| title | A Gauss-Newton Method with No Additional PDE Solves Beyond Gradient Evaluation for Large-Scale PDE-Constrained Inverse Problems |
| topic | Optimization and Control Numerical Analysis 65K10, 86A15, 86A22 |
| url | https://arxiv.org/abs/2603.06899 |