{ "@context": { "@language": "en", "@vocab": "https://schema.org/", "conformsTo": "dct:conformsTo", "cr": "http://mlcommons.org/croissant/", "dataType": { "@id": "cr:dataType", "@type": "@vocab" }, "dct": "http://purl.org/dc/terms/", "prov": "http://www.w3.org/ns/prov#", "rai": "http://mlcommons.org/croissant/RAI/", "sc": "https://schema.org/", "value": { "@id": "cr:value", "@type": "@json" }, "recordSet": "cr:recordSet", "field": "cr:field", "includes": "cr:includes", "source": "cr:source", "fileSet": "cr:fileSet", "extract": "cr:extract", "column": "cr:column" }, "@type": "sc:Dataset", "name": "Poisson_Multimode PosteriorDataset", "description": "PosteriorBench v2.0 Hugging Face Arrow posterior-test dataset for the Poisson_Multimode inverse problem. It contains 10 validation cases and 490 test cases. Each case stores canonical reference fields a_ref and u_ref, optional observation masks and metadata, 100 posterior samples for a and u, and normalized posterior weights. Normalization statistics are intentionally taken from the linked training dataset data/PBench/PDEFieldDataset_hf/Poisson_Multimode.", "conformsTo": [ "http://mlcommons.org/croissant/1.1", "http://mlcommons.org/croissant/RAI/1.0" ], "url": "https://huggingface.co/datasets/anonymousmay/PosteriorBench", "license": "https://creativecommons.org/licenses/by/4.0/", "creator": { "@type": "Organization", "name": "PosteriorBench / DDIS contributors", "url": "https://github.com/neuraloperator/FunDPS-Physics-Guidance" }, "publisher": { "@type": "Organization", "name": "PosteriorBench / DDIS contributors", "url": "https://github.com/neuraloperator/FunDPS-Physics-Guidance" }, "dateCreated": "2026-05-07", "datePublished": "2026-05-07", "dateModified": "2026-05-07", "version": "2.0", "keywords": [ "Poisson equation", "partial differential equation", "inverse problems", "posterior sampling", "diffusion models", "scientific machine learning", "uncertainty quantification" ], "distribution": [ { "@type": "cr:FileSet", "@id": "posterior-arrow-shards", "includes": "*/data-*.arrow", "encodingFormat": "application/vnd.apache.arrow.stream" }, { "@type": "cr:FileObject", "@id": "test/data-00000-of-00014.arrow", "contentUrl": "test/data-00000-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "0a37ef90280e64963e6186b073e7d1e90fa52a0f0244af86e50806d8d77ebbe8" }, { "@type": "cr:FileObject", "@id": "test/data-00001-of-00014.arrow", "contentUrl": "test/data-00001-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "9e9ba19c68a808a41ac215626abd70c3a1dffe3758a7f47756cce7794993a613" }, { "@type": "cr:FileObject", "@id": "test/data-00002-of-00014.arrow", "contentUrl": "test/data-00002-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "057c517ce7d7406f2eb8c1a02fbfac5a86cfd6e0d9fcc2b4de120b2ef60d7d33" }, { "@type": "cr:FileObject", "@id": "test/data-00003-of-00014.arrow", "contentUrl": "test/data-00003-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "18dbfefca6ecee4188182b41579f0b629a1bd862099e95825cde771dcca1d4c9" }, { "@type": "cr:FileObject", "@id": "test/data-00004-of-00014.arrow", "contentUrl": "test/data-00004-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "5a2fbfd3cdb33c23e74fcefbf9e397b87b08dc6a809beb4f4243ba2c4a00b102" }, { "@type": "cr:FileObject", "@id": "test/data-00005-of-00014.arrow", "contentUrl": "test/data-00005-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "e21f69cbd3000ef9ddc498314175f1f2ba67bf4f690e6ff853036cf08f033a81" }, { "@type": "cr:FileObject", "@id": "test/data-00006-of-00014.arrow", "contentUrl": "test/data-00006-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "5ee061ea5273dd0202ac38f6c0424f37fd99182950e355c0d86e240d401e5d16" }, { "@type": "cr:FileObject", "@id": "test/data-00007-of-00014.arrow", "contentUrl": "test/data-00007-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "e1b896b7dc53fd8b582bd25b166a9d3b45dc8995e0d1f26980d956b3593a3d10" }, { "@type": "cr:FileObject", "@id": "test/data-00008-of-00014.arrow", "contentUrl": "test/data-00008-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "7dbcb042d9d6b056df2f99938a27db4d5f533699465ac9001b3888b8be3033a7" }, { "@type": "cr:FileObject", "@id": "test/data-00009-of-00014.arrow", "contentUrl": "test/data-00009-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "e336b411a16c0c41c4e1ae85925575c6b0d5d8ff44994f2f66ace166158e7571" }, { "@type": "cr:FileObject", "@id": "test/data-00010-of-00014.arrow", "contentUrl": "test/data-00010-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "0084744d6c38ca6c215406dc1e1cbdd66ecafcbd4947398244c4946e2e58ff07" }, { "@type": "cr:FileObject", "@id": "test/data-00011-of-00014.arrow", "contentUrl": "test/data-00011-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "96ef05547a79bba2d74eead1e5df9d3203a7203c93c767464c066dc6148fdd7e" }, { "@type": "cr:FileObject", "@id": "test/data-00012-of-00014.arrow", "contentUrl": "test/data-00012-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "3ffe4ddf9e7c95b511a453605c1489f22f600a17a8ace23eaf28a827637dcabb" }, { "@type": "cr:FileObject", "@id": "test/data-00013-of-00014.arrow", "contentUrl": "test/data-00013-of-00014.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "4aa8ea3e3f19734f351d7f7f045501931865ca1a788e692a34df60a31107bc2b" }, { "@type": "cr:FileObject", "@id": "validation/data-00000-of-00001.arrow", "contentUrl": "validation/data-00000-of-00001.arrow", "encodingFormat": "application/vnd.apache.arrow.stream", "sha256": "b057f4731b33afda29fcb1f8f9fabc47371a0d4505a670b6e1a1f820e495848e" }, { "@type": "cr:FileObject", "@id": "dataset_dict.json", "contentUrl": "dataset_dict.json", "encodingFormat": "application/json", "sha256": "36e04f8de625a0445537356be6bf3cba7b031593822216fc6c885da7314a97db" }, { "@type": "cr:FileObject", "@id": "metadata.json", "contentUrl": "metadata.json", "encodingFormat": "application/json", "sha256": "d21851ebe953d99272c2dfd1efda4e5b8508d42a975b3b87e93eb0758d8bdd2d" }, { "@type": "cr:FileObject", "@id": "validation/dataset_info.json", "contentUrl": "validation/dataset_info.json", "encodingFormat": "application/json", "sha256": "88cc942bb295ec880b613a7ea995e8d1034529261d1f4dee156cb9c7b4908e94" }, { "@type": "cr:FileObject", "@id": "validation/state.json", "contentUrl": "validation/state.json", "encodingFormat": "application/json", "sha256": "f147bdf834dd89075b378fa1f7aa299a2b1b2d3b9026c83d0e73f8e67e9b3aa9" }, { "@type": "cr:FileObject", "@id": "test/dataset_info.json", "contentUrl": "test/dataset_info.json", "encodingFormat": "application/json", "sha256": "88cc942bb295ec880b613a7ea995e8d1034529261d1f4dee156cb9c7b4908e94" }, { "@type": "cr:FileObject", "@id": "test/state.json", "contentUrl": "test/state.json", "encodingFormat": "application/json", "sha256": "65162de8d2898575a4cdfcecccee29adabeb7e35348cf4123b667531180f5128" } ], "rai:dataLimitations": "The dataset is synthetic Poisson_Multimode posterior benchmark data at fixed resolution [128, 128]; observations are partial.", "rai:dataBiases": "The data are synthetic and inherit the parameter ranges, resolution, and case selection of their source generators.", "rai:personalSensitiveInformation": "No personal or sensitive information is present.", "rai:dataUseCases": [ "Benchmarking posterior sampling and reconstruction methods for synthetic inverse problems.", "Training or evaluating scientific machine-learning models with PosteriorBench v2.0 loaders.", "Not recommended for claims about real-world physical systems without validation against domain data." ], "rai:dataSocialImpact": "Positive impact is expected primarily through reproducible scientific machine-learning benchmarks for inverse problems.", "rai:hasSyntheticData": true, "prov:wasDerivedFrom": [ { "@id": "urn:posteriorbench:source:poisson_multimode_posterior", "@type": "prov:Entity", "name": "data/PBench/poisson_distribution_data_3e-4.zip", "description": "Raw Poisson posterior case archive converted to PosteriorBench v2.0 validation/test cases." } ], "prov:wasGeneratedBy": [ { "@id": "urn:posteriorbench:activity:poisson_multimode_hf_export", "@type": "prov:Activity", "name": "PosteriorBench v2.0 HF export", "description": "The conversion stores canonical fields and metadata as a Hugging Face Dataset backed by Apache Arrow shards." } ], "recordSet": [ { "@type": "cr:RecordSet", "@id": "poisson_multimode_posterior", "field": [ { "@type": "cr:Field", "@id": "poisson_multimode_posterior/splits", "dataType": "sc:Text", "value": { "validation": 10, "test": 490, "total": 500 } }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/case_id", "dataType": "sc:Text", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "case_id" } } }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/a_ref", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "a_ref" } }, "description": "Reference canonical a field with channels ['a'] and shape [1, 128, 128]." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/u_ref", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "u_ref" } }, "description": "Reference canonical u field with channels ['u'] and shape [1, 128, 128]." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/mask", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "mask" } }, "description": "Observation mask when available; null for full-field or metadata-only observations." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/posterior_samples_a", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "posterior_samples_a" } }, "description": "Posterior samples for a with shape [100, 1, 128, 128]." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/posterior_samples_u", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "posterior_samples_u" } }, "description": "Posterior samples for u with shape [100, 1, 128, 128]." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/posterior_weights", "dataType": "cr:Float32", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "posterior_weights" } }, "description": "Normalized posterior weights with length 100." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/params", "dataType": "sc:Text", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "params" } }, "description": "Case-level generation parameters when available." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/metadata", "dataType": "sc:Text", "source": { "fileSet": { "@id": "posterior-arrow-shards" }, "extract": { "column": "metadata" } }, "description": "Case-level source, observation, and conversion metadata." }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/training_dataset", "dataType": "sc:Text", "value": "data/PBench/PDEFieldDataset_hf/Poisson_Multimode" }, { "@type": "cr:Field", "@id": "poisson_multimode_posterior/normalization", "dataType": "sc:Text", "value": "Use DatasetNormalizer.from_training_dataset(training_dataset); PosteriorDataset does not carry independent normalization stats." } ] } ] }