MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving
Partial differential equation (PDE) solvers underpin scientific computing, but real-world deployment is bounded by compute. Classical Monte Carlo solvers such as Walk-on-Spheres (WoS) are unbiased and geometry-agnostic but are slow. Learned solvers are fast but biased and brittle under distribution shift. We present \textbf{MC$^2$}, a hybrid WoS-Neural Network (WoS-NN) PDE solver that treats a low-budget Monte Carlo solution as a structured estimator of the true field and learns a single-pass neural correction to recover a high-fidelity solution. MC$^2$ matches the accuracy of solutions using over $1000\times$ more Monte Carlo compute, outperforming all evaluated classical, denoising, and...
| Authors | Ethan Hsu, Hong Meng Yam, Ivan Ge |
|---|---|
| Primary category | cs.LG |
| Published | 10 May 2026 |
| Last updated at source | 10 May 2026 |
Popularity, last 2 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 18 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.