Neural Caches for Monte Carlo Partial Differential Equation Solver (original) (raw)

We combine Neural Field with Monte Carlo method, provide a faster and more accurate PDE solver.

We visualize a slice of the solution to an elliptic PDE within a dragon-shaped boundary. Our hybrid solver can reduce the error of the neural field baseline, while achieving lower variance compared to the Walk-on-Spheres (VCWoS) method when working within the constraints of a limited computing budget

Introduction

Solving PDEs without discretization is valuable in many graphics application. Monte Carlo PDE solvers are un-biased but suffer from high variance. In contrast, Neural Fields-based solvers offer faster inference but often yield biased outcomes. We propose to use neural field caches to reduce variance in Monte Carlo PDE solvers.

Method

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