Solving Inverse PDE Problems Using Grid-Free Monte Carlo Estimators
Event details
| Date | 18.06.2024 |
| Hour | 15:00 › 17:00 |
| Speaker | Ekrem Fatih Yilmazer |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Mark Pauly
Thesis advisor: Prof. Wenzel Jakob
Co-examiner: Prof. Nicolas Flammarion
Abstract
Modeling physical phenomena such as heat transport and diffusion relies heavily on the numerical solution of partial differential equations (PDEs). Traditional PDE solvers that utilize the finite element method involve a domain meshing step, which can be both fragile and expensive. Alternatively, grid-free Monte Carlo methods stochastically sample paths to create an unbiased estimator of the solution. Several recent works showed that there is a striking similarity between the physically based rendering algorithms.
My research aims to solve inverse PDE problems using these Grid-Free Monte Carlo estimators. Given the solution information in a region inside the domain, I try to reconstruct the parameters of the PDE. Due to the significant resemblance of MC PDE solvers to the light simulation, the methods in differentiable rendering is a good starting point to attack inverse PDE problems.
In this brief write-up, I will introduce some of the MC forward PDE solvers and describe the similarities between the physically based rendering.
Background papers
Monte Carlo Geometry Processing
https://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf
Grid-Free Monte Carlo PDEs with Spatially Varying Coefficients
www.cs.cmu.edu/~kmcrane/Projects/VariableCoefficientWoS/VariableCoefficientWoS.pdf
Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions
https://www.cs.cmu.edu/~kmcrane/Projects/WalkOnStars/WalkOnStars.pdf
Exam president: Prof. Mark Pauly
Thesis advisor: Prof. Wenzel Jakob
Co-examiner: Prof. Nicolas Flammarion
Abstract
Modeling physical phenomena such as heat transport and diffusion relies heavily on the numerical solution of partial differential equations (PDEs). Traditional PDE solvers that utilize the finite element method involve a domain meshing step, which can be both fragile and expensive. Alternatively, grid-free Monte Carlo methods stochastically sample paths to create an unbiased estimator of the solution. Several recent works showed that there is a striking similarity between the physically based rendering algorithms.
My research aims to solve inverse PDE problems using these Grid-Free Monte Carlo estimators. Given the solution information in a region inside the domain, I try to reconstruct the parameters of the PDE. Due to the significant resemblance of MC PDE solvers to the light simulation, the methods in differentiable rendering is a good starting point to attack inverse PDE problems.
In this brief write-up, I will introduce some of the MC forward PDE solvers and describe the similarities between the physically based rendering.
Background papers
Monte Carlo Geometry Processing
https://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf
Grid-Free Monte Carlo PDEs with Spatially Varying Coefficients
www.cs.cmu.edu/~kmcrane/Projects/VariableCoefficientWoS/VariableCoefficientWoS.pdf
Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions
https://www.cs.cmu.edu/~kmcrane/Projects/WalkOnStars/WalkOnStars.pdf
Practical information
- General public
- Free