Presentation
Off-Centered WoS-Type Solvers with Statistical Weighting
DescriptionStochastic solvers have emerged as a powerful alternative to traditional discretization-based methods for solving partial differential equations (PDEs), especially in geometry processing and graphics. While off-centered estimators enhance sample reuse in Monte Carlo solvers, they introduce correlation artifacts and bias when Green’s functions are approximated. In this paper, we propose a statistically weighted off-centered Monte Carlo estimator that leverages local similarity filtering to selectively combine samples across neighboring evaluation points. Our method balances bias and variance through a principled weighting strategy that suppresses unreliable estimators. We demonstrate our approach's effectiveness on various PDEs—including screened Poisson equations—and boundary conditions, achieving consistent improvements over existing solvers such as vanilla Walk on Spheres, mean value caching, and boundary value caching. Our method also naturally extends to gradient field estimation and mixed boundary problems.
Event Type
Technical Papers
TimeWednesday, 17 December 20251:53pm - 2:04pm HKT
LocationMeeting Room S426+S427, Level 4