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math.ST2026
PDE-constrained inverse problems at the rate via debiased physics-informed neural networks
Yves Atchade, Debarghya Mukherjee
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 Neu…
math.ST2024
On the estimation rate of Bayesian PINN for inverse problems
Yi Sun, Debarghya Mukherjee, Yves Atchade
Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine lea…