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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.14858 |
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| _version_ | 1866915743393644544 |
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| author | Kanchi, Rohit Sunil He, Sicheng |
| author_facet | Kanchi, Rohit Sunil He, Sicheng |
| contents | Inverse problems in computational physics often require matching high-dimensional spatio-temporal fields, leading to prohibitive computational costs and ill-conditioned optimizations. We introduce modal-centric field inversion (MCFI), a paradigm that reformulates inverse problems in the reduced space of proper orthogonal decomposition (POD) modes rather than the full physical state space. By targeting dominant flow structures instead of point-wise field values, MCFI provides a compact, physically meaningful objective that naturally regularizes the inversion and dramatically reduces computational burden. Central to this framework is the differentiable POD: an adjoint-based method that efficiently computes sensitivities of POD modes with respect to model parameters, enabling gradient-based optimization in the modal space. We demonstrate MCFI on a one and two-dimensional modified viscous Burger's equation, optimizing spatially varying coefficients to match target dynamics through mode-matching. The adjoint formulation achieves computational cost independent of parameter dimension, in contrast to finite-difference approaches that scale linearly. MCFI establishes a foundation for scalable inverse design and model calibration in unsteady, high-dimensional systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modal-Centric Field Inversion via Differentiable Proper Orthogonal Decomposition Kanchi, Rohit Sunil He, Sicheng Numerical Analysis Inverse problems in computational physics often require matching high-dimensional spatio-temporal fields, leading to prohibitive computational costs and ill-conditioned optimizations. We introduce modal-centric field inversion (MCFI), a paradigm that reformulates inverse problems in the reduced space of proper orthogonal decomposition (POD) modes rather than the full physical state space. By targeting dominant flow structures instead of point-wise field values, MCFI provides a compact, physically meaningful objective that naturally regularizes the inversion and dramatically reduces computational burden. Central to this framework is the differentiable POD: an adjoint-based method that efficiently computes sensitivities of POD modes with respect to model parameters, enabling gradient-based optimization in the modal space. We demonstrate MCFI on a one and two-dimensional modified viscous Burger's equation, optimizing spatially varying coefficients to match target dynamics through mode-matching. The adjoint formulation achieves computational cost independent of parameter dimension, in contrast to finite-difference approaches that scale linearly. MCFI establishes a foundation for scalable inverse design and model calibration in unsteady, high-dimensional systems. |
| title | Modal-Centric Field Inversion via Differentiable Proper Orthogonal Decomposition |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.14858 |