Please note: This master’s research paper presentation will take place online.
Haochen Gan, Master’s candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Toshiya Hachisuka
Partial differential equations underlie a wide range of computer graphics tasks, from geometry processing and diffusion-based editing to fluid simulation. The dominant numerical approach, mesh-based discretisation, becomes expensive and brittle on geometrically complex domains, where meshing itself is a substantial computation. Monte Carlo PDE solvers offer an alternative: they express the solution as the expectation of a random variable and estimate it by averaging stochastic samples, with error scaling independent of spatial dimension.
This essay surveys the grid-free branch of Monte Carlo PDE solvers, which estimates the solution at a single query point using only local geometric queries. We organise the literature around the integral and probabilistic representations underlying each solver family, estimator design and variance reduction, and practical considerations for parallel and GPU implementations.
Attend this master’s research paper presentation virtually on Zoom.