Numerous scientific and engineering applications require solutions to boundary value
problems (BVPs) involving elliptic partial differential equations, such as the Laplace or …

Despite significant advancements in Neural Radiance Fields (NeRFs), the renderings may
still suffer from aliasing and blurring artifacts, since it remains a fundamental challenge to …

We introduce a Monte Carlo method for computing derivatives of the solution to a partial
differential equation (PDE) with respect to problem parameters (such as domain geometry or …

The idea of using a neural network to represent continuous vector fields (ie, neural fields)
has become popular for solving PDEs arising from physics simulations. Here, the classical …

We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient
solution of high-dimensional Poisson equations. Leveraging stochastic representations and …

Partial differential equations can model diverse physical phenomena including heat
diffusion, incompressible flows, and electrostatic potentials. Given a description of an …

This paper presents a method to leverage arbitrary neural network architecture for control
variates. Control variates are crucial in reducing the variance of Monte Carlo integration, but …

Walk on stars (WoSt) has shown its power in being applied to Monte Carlo methods for
solving partial differential equations, but the sampling techniques in WoSt are not …

Herein, we present a novel method that utilizes neural networks to improve solution
generation from Monte Carlo Partial Differential Equation solvers. Current Monte Carlo PDE …