Walk on Spheres

Boundary Value Caching for Walk on Spheres

Bailey Miller, Rohan Sawhney, Keenan Crane, Ioannis Gkioulekas

Journal SIGGRAPH 2023 Animation & Simulation
Monte Carlo Walk on Spheres PDE Solver Boundary Integral Equation Sample Reuse

Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions

Rohan Sawhney, Bailey Miller, Ioannis Gkioulekas, Keenan Crane

Journal SIGGRAPH 2023 Animation & Simulation
Monte Carlo Walk On Spheres PDE Solver Boundary Integral Equation Grid-Free Simulation

A Differential Monte Carlo Solver For the Poisson Equation

Zihan Yu, Lifan Wu, Zhiqian Zhou, Shuang Zhao

Conference SIGGRAPH 2024 Animation & Simulation
Monte Carlo Method Poisson Equation Walk On Spheres Differentiable PDE Solver Shape Optimization

Conformal First Passage for Epsilon-free Walk-on-Spheres

Paul Himmler, Tobias Günther

Journal SIGGRAPH 2025 Rendering
Monte Carlo Walk On Spheres Partial Differential Equations First Passage Conformal Maps Diffusion Curves

Solving partial differential equations in participating media

Bailey Miller, Rohan Sawhney, Keenan Crane, Ioannis Gkioulekas

Journal SIGGRAPH 2025 Animation & Simulation
Monte Carlo Walk On Spheres Partial Differential Equations Participating Media Volume Rendering

Unbiased Differential Visibility Using Fixed-Step Walk-on-Spherical-Caps And Closest Silhouettes

Lifan Wu, Nathan Morrical, Sai Praveen Bangaru, Rohan Sawhney, Shuang Zhao, Chris Wyman, Ravi Ramamoorthi, Aaron E. Lefohn

Journal SIGGRAPH 2025 Rendering
Differentiable Rendering Differential Visibility Warped-Area Reparameterization Walk On Spheres Monte Carlo PDE Solver Closest Silhouette Query

Fast Cutting of Cage Based Deformation with Walk on Spheres

Hossam Saeed, Michael Lambiri, Teseo Schneider, Derek Nowrouzezahrai, Paul G. Kry

Conference meta-only SIGGRAPH 2026 Geometry & Modeling
Walk On Spheres Cage Deformation Monte Carlo Geometry Processing Mesh Cutting

Gradient Domain Reconstruction for Monte Carlo PDE Solvers

Jiaqi Wu, Xuejun Hu, Shuang Zhao, Kun Xu

Journal SIGGRAPH 2026 Animation & Simulation
Monte Carlo Method Poisson Equation Walk On Spheres Gradient-Domain Rendering Variance Reduction

Probe-based Walk on Spheres for Efficient Path Reusing

Wanchao Huang, Yutian Zhu, Qing Fang, Ligang Liu

Journal SIGGRAPH 2026 Rendering
Walk On Spheres Monte Carlo PDE Solver Variance Reduction Grid-Free Path Reuse

Walk on Decomposed Subdomains: A Hybrid Monte Carlo-Deterministic Solver for Elliptic PDEs

Clément Jambon, Mohammad Sina Nabizadeh, Mina Konaković Luković

Journal SIGGRAPH 2026 Animation & Simulation
Monte Carlo Walk On Spheres Elliptic PDE Domain Decomposition Markov Chain Poisson Kernel

Walking on Spheres and Talking to Neighbors: Variance Reduction for Laplace's Equation

Michael T. Czekanski, Benjamin J. Faber, Margaret E. Fairborn, Adelle M. Wright, David S. Bindel

Conference SIGGRAPH 2026 Rendering
Walk On Spheres Monte Carlo Variance Reduction Laplace Equation Caching

Discontinuity-Aware 2D Neural Fields

Yash Belhe, Michaël Gharbi, Matthew Fisher, Iliyan Georgiev, Ravi Ramamoorthi, Tzu-Mao Li

Journal SIGGRAPH Asia 2023 Neural & Generative
Neural Fields Image Compression Discontinuity Walk on Spheres Physics-Informed Neural Network

Neural Caches for Monte Carlo Partial Differential Equation Solvers

Zilu Li, Guandao Yang, Xi Deng, Christopher De Sa, Bharath Hariharan, Steve Marschner

Conference SIGGRAPH Asia 2023 Animation & Simulation
Walk On Spheres Neural Field Monte Carlo PDE Solver Variance Reduction

Differential Walk on Spheres

Bailey Miller, Rohan Sawhney, Keenan Crane, Ioannis Gkioulekas

Journal SIGGRAPH Asia 2024 Rendering
Walk on Spheres Monte Carlo Differentiable Simulation Shape Optimization Partial Differential Equation Inverse Problem

Projected Walk on Spheres: A Monte Carlo Closest Point Method for Surface PDEs

Ryusuke Sugimoto, Nathan D. King, Toshiya Hachisuka, Christopher Batty

Conference SIGGRAPH Asia 2024 Geometry & Modeling
Monte Carlo PDE Walk on Spheres Surface PDE Closest Point Method Diffusion Curves

Solving Inverse PDE Problems using Grid-Free Monte Carlo Estimators

Ekrem Fatih Yilmazer, Delio Vicini, Wenzel Jakob

Journal SIGGRAPH Asia 2024 Rendering
Walk on Spheres Monte Carlo Differentiable Simulation Inverse Problems Path Replay Backpropagation

Harmonic Caching for Walk on Spheres

Zihong Zhou, Eugene d'Eon, Rohan Sawhney, Wojciech Jarosz

Journal meta-only SIGGRAPH Asia 2025 Rendering
Walk On Spheres Monte Carlo Partial Differential Equations Variance Reduction Harmonic Functions Grid Free Solver

Off-Centered WoS-Type Solvers with Statistical Weighting

Anchang Bao, Jie Xu, Enya Shen, Jianmin Wang

Conference SIGGRAPH Asia 2025 Geometry & Modeling
Monte Carlo PDE Solver Walk On Spheres Variance Reduction Statistical Weighting Screened Poisson Equation Geometry Processing

Robust Derivative Estimation with Walk on Stars

Zihan Yu, Rohan Sawhney, Bailey Miller, Lifan Wu, Shuang Zhao

Journal meta-only SIGGRAPH Asia 2025 Rendering
Walk On Stars Walk On Spheres Monte Carlo Methods Partial Differential Equations Derivative Estimation Neumann Boundary Conditions Grid Free Solvers