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PDE-constrained inverse problems at the $\sqrt{n}$ rate via debiased physics-informed neural networks

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

We study the problem of estimating unknown parameters in PDE-constrained inverse problems from noisy observations, where the PDE solution is approximated using Physics-Informed Neural Networks (PINNs). While PINNs have demonstrated remarkable empirical success, existing estimators often inherit the slow nonparametric convergence rate of the neural-network solution, leading to biased and statistically inefficient inference for the finite-dimensional parameters of interest. To address this, we propose a two-step debiased estimation procedure that combines neural-network-based nonparametric estim

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