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Constrained sampling closes this gap, enforcing such constraints exactly at inference time without retraining, but at a computational cost: projection, correction, and trajectory-optimization steps are repeated during sampling, with these steps becoming expensive for nonlinear constraints. Standard ML frameworks exacerbate this: their dense tensor algebra and limited sparse solver composability obscure the structure that physical constraints naturally induce, making efficient batched nonlinear optimization difficult to realize in practice. We address this bottleneck by exploiting the structure that sample-wise batching and local PDE couplings induce in the projection subproblems -- namely, block-spars","title":"SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling","url":"https://arxiv.org/abs/2607.00095","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.00095v1 Announce Type: cross \nAbstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics. Constrained sampling closes this gap, enforcing such constraints exactly at inference time without retraining, but at a computational cost: projection, correction, and trajectory-optimization steps are repeated during sampling, with these steps becoming expensive for nonlinear constraints. Standard ML frameworks exacerbate this: their dense tensor algebra and limited sparse solver composability obscure the structure that physical constraints naturally induce, making efficient batched nonlinear optimization difficult to realize in practice. We address this bottleneck by exploiting the structure that sample-wise batching and local PDE couplings induce in the projection subproblems -- namely, block-spars","title":"SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-02T04:43:28Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.00095"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b8d874db802fb0e9328e46f951ae69130d19e70a8311659c0058aba4f2c75834797cab0f8fa662b00d35f339d4bc17df4c26f81e68bf50b33b18378aa2753203","signer":"crovia.substrate","subject":{"observed_at":"2026-07-02T04:43:28Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.00095"},"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":"497837a5540adecfea7bb1a89edf110b2ddcdf01bd1f5a73aea908ad3b61f6f2","leaf_index":271977,"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":"50958a7bead1516d29177666780f1df876cd37cf6ae52e03c10dbf508dbebd8e","side":"left"},{"sibling":"bf373ea31d916ca87cd9295aaa3627c60e9ca2a93f7d23d60bf00a947f22c6d3","side":"right"},{"sibling":"27ab032389cfc4f79d1823b70459701c4d0986a5a6dcc52c911e8b5a93963cc6","side":"right"},{"sibling":"9ae2cab41c06d82e9840829e57bd7a2a47ab6566c2b2f845e60483a1a0f78f08","side":"left"},{"sibling":"f746b927d1f90ae3862bcf56b43ce81c1e825efaeba580cc981b9648dd555c28","side":"right"},{"sibling":"c25f18d33f4ad3f321fbcc471335c7d8875df72b3401ae191213309c57c4d3fb","side":"left"},{"sibling":"bba3920d4d73572ccae4aab47102490e036c6245a6d1cb8a6c5b92b702d7f20a","side":"left"},{"sibling":"245706846217c65709d33d0c2ef53806eee8ea674294e4e08c1d4f19cee09ac7","side":"right"},{"sibling":"155ae596a5c6a5260be50ff412642fbd25f4587b43e04c56950c1dc544719be1","side":"right"},{"sibling":"4cfdd7f7072619c015edc477162c2cf29c6f70370acb8dbddf1eb590876d82fe","side":"left"},{"sibling":"43990c9db8fcb3172d821965dfac69152981af4108b8dc87bd32f15c0e56f4cf","side":"left"},{"sibling":"15dbacc2e5845fe3bb835797bb7647ab6f091e79adadd39f40c636980716c622","side":"right"},{"sibling":"7ecc1d0d471643b88d886db58cb02a77af4d1495674760c3867834550b143757","side":"right"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"7b681d50e7d0a7b8d2a749507aed58030072539a90fab18de4f698743685cc00","side":"right"},{"sibling":"9b262645232510ff15bb7325ab858256f2914f711d2726caeafd49f5ca0fb7a9","side":"right"},{"sibling":"5bd94446b5721b713c5e4dcf4624b9bc682657ab2784af927caae7b80c297d7d","side":"right"},{"sibling":"21ac0b7091fe1133859bcd17b4f8da2fe37a2489d472dad508305740b483221b","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":272319,"merkle_root":"dd4fa4deb1f207e8a7756821b4f940f39e9f06a25e6fa8500a21dd403318a5a7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260702T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-02T05:38:06Z","sig_algorithm":"ed25519","signature":"68eb2e3bbc0f593bea7b5c3c110c90b6f4fe4fd8277d8dee7c866ba0471c1a50684aa4539c8a493e6d9c9202d8c03f4d897a0df3477e9ecd5b0ff03eb1016f00","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_4a83eb58fc33a4ce2218404d857aef4243008be8139869ae81c7739cf827e931"}}