# PDE-Constrained Inverse Problem **Entity class:** Mathematical inference method ## Definition A **PDE-constrained inverse problem** infers hidden parameters or states from observations while requiring candidate explanations to satisfy a partial-differential-equation model of the underlying physics. Each inference can require many expensive forward solves. ## Relationships - **specialization of:** [[wiki/Inverse Problem|Inverse Problem]]. - **accelerated by:** [[wiki/Reduced-Order Modeling|Reduced-Order Modeling]] and [[wiki/Scientific Machine Learning|Scientific Machine Learning]]. - **example:** parametrized [[wiki/Neutron Transport Equation|neutron-transport]] inverse problems. - **qualified by:** [[wiki/Verification Validation and Uncertainty Quantification|Uncertainty Quantification]]. ## Sources / Provenance - [Sheriffdeen et al. — Accelerating PDE-constrained Inverse Solutions, 2019](https://arxiv.org/abs/1912.08864)