Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Solving Poisson Equations using Neural Walk-on-Spheres
Authors: Hong Chul Nam, Julius Berner, Anima Anandkumar
ICML 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In several challenging, high-dimensional numerical examples, we demonstrate the superiority of NWo S in accuracy, speed, and computational costs. Compared to commonly used PINNs, our approach can reduce memory usage and errors by orders of magnitude. Furthermore, we apply NWo S to problems in PDEconstrained optimization and molecular dynamics to show its efficiency in practical applications. |
| Researcher Affiliation | Academia | 1ETH Zurich 2Caltech. Correspondence to: Hong Chul Nam <EMAIL>, Julius Berner <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Training of vanilla NWo S method |
| Open Source Code | Yes | Our Py Torch code can be found at https://github. com/bizoffermark/neural_wos. |
| Open Datasets | No | The paper defines mathematical problems (Laplace Equation, Poisson Equation, Committor Function) with analytical solutions for evaluation, rather than using external publicly available datasets with access information. |
| Dataset Splits | No | The paper describes sampling points in the domain and on the boundary for training and evaluating on unseen points via MC integration, but it does not specify explicit train/validation/test dataset splits with percentages or counts. |
| Hardware Specification | Yes | The experiments have been conducted on A100 GPUs. |
| Software Dependencies | No | The paper states 'We implemented all methods in Py Torch' but does not provide a specific version number for PyTorch or any other software dependencies. |
| Experiment Setup | Yes | For all our training, we use the Adam optimizer and limit the runtime to 25d + 750 seconds for a fair comparison... We employ an exponentially decaying learning rate... We choose a feedforward neural network with residual connections, 6 layers, a width of 256, and a GELU activation function. We also perform the grid search for the boundary loss penalty term, i.e., β {0.5, 1, 5, 50, 100, 500, 1000, 5000}. We further include the batch size m {2i}17 i=7 in our grid search. |