{"url":"/dataset/poisson-equation","name":"Poisson Equation","full_name":"Poisson Equation with unstructured grid","description_markdown":"\\subsection{Poisson Equation}\r\nThe Poisson equation with Dirichlet boundary conditions is studied:\r\n\\begin{align}\r\n    -\\Delta u &= f, \\quad \\text{in } \\Omega = [0,1]^2, \\\\\r\n    u &= 0, \\quad \\text{on } \\partial \\Omega,\r\n\\end{align}\r\nwhere \\(f\\) consists of a Gaussian superposition, with parameters \\(\\mu_{x,i}, \\mu_{y,i} \\sim \\text{U}(0,1)\\) and \\(\\sigma_i \\sim \\text{U}(0.025, 0.1)\\). The dataset includes 4000 training, 500 validation, and 500 test samples.","description_withheld":null,"homepage":"https://github.com/lizhihao2022/AMG","introduced_date":"2024-11-18","introduced_date_note":null,"introduced_by":{"paper":"/paper/harnessing-scale-and-physics-a-multi-graph","title":"Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries","first_author":"Zhihao LI","url":null},"license":null,"modalities":[],"tasks":[],"languages":[],"variants":["Poisson Equation"],"data_loaders":[],"num_papers_in_archive":2,"source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28"},"benchmarks":[],"papers_with_a_benchmark_row":[],"syntology_totals":{"read_at":"2026-09-24T18:15:14+00:00","papers_with_samples":0,"samples_harvested":0,"samples_ran":0,"samples_unverified":0,"pointer_only_for_licence":0,"papers_with_no_sample_that_ran":0,"note":"the per-paper counts above, summed; not a rate"},"papers_note":"The archive never published its papers-using-dataset list; these are papers with a leaderboard row on this dataset's benchmarks."}