We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling this …
Computing derivatives of path integrals under evolving scene geometry is a fundamental problem in physics-based differentiable rendering, which requires differentiating discontinuities in the visibility function. Warped area reparameterization is a …
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 boundary conditions). Derivatives can be evaluated at arbitrary …
We present a neural network-based simulation super-resolution framework that can efficiently and realistically enhance a facial performance produced by a low-cost, real-time physics-based simulation to a level of detail that closely approximates that …
Numerous scientific and engineering applications require solutions to boundary value problems (BVPs) involving elliptic partial differential equations, such as the Laplace or Poisson equations, on geometrically intricate domains. We develop a Monte …
Grid-free Monte Carlo methods such as walk on spheres can be used to solve elliptic partial differential equations without mesh generation or global solves. However, such methods independently estimate the solution at every point, and hence do not …
Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite basis. Such …