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However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by B\\'ezier surfaces, and the generator tries to learn the coefficients of each B\\'ezier surface to further combine multiple B\\'ezier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transf","title":"IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry","url":"https://arxiv.org/abs/2607.11497","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.11497v1 Announce Type: cross \nAbstract: Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by B\\'ezier surfaces, and the generator tries to learn the coefficients of each B\\'ezier surface to further combine multiple B\\'ezier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transf","title":"IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-14T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.11497"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:47436808f84a3c32255dea275f970cd8786ae1d0ce4c14948676968af1baa2062f6e7cda2e17b7e9671fe583689f2b16d10e70f2292e2c4c509aa0b078eec505","signer":"crovia.substrate","subject":{"observed_at":"2026-07-14T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.11497"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"b2658b477e7672c36d076591a3d2cfd5315d7596db663faa4e71d3346030707a","leaf_index":313082,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"5ef1e8fd54e04db0e9585f80efba7f04be70135251557431cb59df1ffdd16513","side":"right"},{"sibling":"5923dc68ee5f9bd3e4d7a2bda27ec67c3f6716d5a5d1a5243dab9aa462fb16d9","side":"left"},{"sibling":"1f3096ed0bc1c9454468e05a14500923291703f79a4cec4a8ff03af31b9c5e58","side":"right"},{"sibling":"3a23a23d7cfc17ee5890113ee0a95f9beda7cad61b3095846e4a6ba29123d3e8","side":"left"},{"sibling":"e10ada4905c9b80414b50a75bbfc399e85af380daad8c6ebf3e2eb0973e7b574","side":"left"},{"sibling":"3eee7f7de91efd32b61ea70407b08cf9729fb081cad6b2c526dd7be7dde94eb8","side":"left"},{"sibling":"baeef0520c1ff97b73a9d4a5e9b7ae2c4f3b622a20eca633ca7243f629bd2722","side":"left"},{"sibling":"018f1c17268dcf6ba6107e8d52410ad70a49124aa289c7dcb4ed6c05713b1cf0","side":"left"},{"sibling":"ca17e703a3fca19bfbb090cbed9e2450594a9c237665dd9a566195d3ef3072f7","side":"right"},{"sibling":"8393dc03644000353c5d503b6ec261c022cd2aa85a649223916153bc8af2dc75","side":"left"},{"sibling":"1627ce6908965f2e5fbc7c16bc8e247867478c587014561d0de1359dc2dc0afc","side":"left"},{"sibling":"74e1ba9fd48bdd0f52777dd5b56c10706e73f42629013748eca13ef113cd59db","side":"right"},{"sibling":"682fd39539db5bce908d0ab6f180374728fed6b34a9a8c87c7b4eb5a726e30b8","side":"right"},{"sibling":"184927f71d667ac0c6ebeadb33394626973738b9107c6dc3c0c4949b44acf295","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"c4c189d79669979b59d9aa976ee249c54a7e065b4a05bf49463459cc7f37428e","side":"right"},{"sibling":"19475e206bdf2698769a286db2c97c4d3f089741319f9b29a139038c6e511975","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":313381,"merkle_root":"5f7d48580373d0ab0bc6bdf34f26de442f9a86d130946f7ee45addd1a55cb9f4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260714T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-14T05:38:23Z","sig_algorithm":"ed25519","signature":"97364224142ed1b2a8925fed1bfba2e0a8a6a15f8ca0999b934846ad83584a78c7f0f5cd09dbc1c938b35383fcc5c8fa4b723118e30916628879d1c5fd3a9908","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_c5ea6936adff30ff3627d4d17451c345e37d6fed6ab5469621c09cd9ff6c128a"}}