"WoS-NN: Collaborating Walk-on-Spheres with Machine Learning to Solve Elliptic PDEs"
Wednesday, Mar 26, 2025, Schedule:
- Nespresso & Teatime - 417 DSL Commons
- 03:00 to 03:30 PM Eastern Time (US and Canada)
- Colloquium - 499 DSL Seminar Room
- 03:30 to 04:30 PM Eastern Time (US and Canada)
Click Here to Join via Zoom
Meeting # 942 7359 5552
Zoom Meeting # 942 7359 5552
Abstract:
Solving elliptic partial differential equations (PDEs) is a fundamental step in various scientific and engineering studies. As a classic stochastic solver, the Walk on Spheres (WoS) method is a well-established and efficient algorithm that provides accurate local estimates for PDEs. However, limited by the curse of dimensionality, WoS may not offer sufficiently precise global estimations, which becomes more serious in high-dimensional scenarios. Recent developments in machine learning offer promising strategies to address this limitation. By integrating machine learning techniques with WoS and space discretization approaches, we developed a novel stochastic solver, WoS-NN. This new method solves elliptic problems with Dirichlet boundary conditions, facilitating precise and rapid global solutions and gradient approximations. A typical experimental result demonstrated that the proposed WoS-NN method provides accurate field estimations, reducing 76.32% errors while using only 8% of path samples compared to the conventional WoS method, which saves abundant computational time and resource consumption. This seminar will include a general description of stochastic solvers for different PDEs, the design and execution of WoS-NN, and experiment results indicating the fascination of our method.
