4 papers
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…
Data-driven rainfall prediction at a regional scale: a case study with Ghana
Indrajit Kalita, Lucia Vilallonga, Yves Atchade
With a warming planet, tropical regions are expected to experience the brunt of climate change, with more intense and more volatile rainfall events. Currently, state-of-the-art num…
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…
A statistical perspective on algorithm unrolling models for inverse problems
Yves Atchade, Xinru Liu, Qiuyun Zhu
We consider inverse problems where the conditional distribution of the observation given the latent variable of interest (also known as the forward model) is kn…