Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects

In three linesComprehensive review of AI methods for solving inverse partial differential equation (PDE) problems. Covers three categories: inverse problems, inverse design, and control. Applications: medical imaging, geophysics, aerodynamics, thermal systems. Challenges: physics-informed architectures, limited real-world data, uncertainty quantification, inverse foundation models.

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