MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving

arXiv:2605.09288v2 Announce Type: replace-cross Abstract: Partial differential equation (PDE) solvers underpin modern computer graphics, geometry processing, and scientific computing. Classical Monte Carlo PDE solvers such as Walk-on-Spheres (WoS) provide mesh-free estimations that are unbiased, but with accuracy limited by sampling and numerical approximation. Learned solvers are fast but biased and brittle under distribution shift. We therefore present MC$^2$, a hybrid Neural Network-Monte Carlo PDE solver that treats a low-budget Monte Carlo solution as a structured estimator of the true fi

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