Inverse PDE Problem

Inverse partial differential equation (PDE) problems aim to determine unknown parameters or initial conditions of a PDE system from observed data, often involving noisy or incomplete measurements. Current research heavily utilizes machine learning, employing architectures like physics-informed neural networks (PINNs), neural operators, and generative models (e.g., diffusion models) to solve these challenging inverse problems, with a strong focus on improving accuracy, efficiency, and uncertainty quantification. These advancements are significantly impacting various scientific fields and engineering applications by enabling more robust and efficient solutions to problems involving parameter estimation, data assimilation, and image reconstruction from incomplete or noisy data.