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For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dyna","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","url":"https://arxiv.org/abs/2605.25413","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.25413v3 Announce Type: replace-cross \nAbstract: Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dyna","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-08T04:44:02Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.25413"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:cdd0a846f85bbd6eb09564b684a107c00cecc2224ac99f22a2ff17e94db953c09e513ceec3cb1bec3982056c3c41f297f6130d3ec18e3ec6ff724d22666c2909","signer":"crovia.substrate","subject":{"observed_at":"2026-06-08T04:44:02Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.25413"},"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":"a26249573a18c398967003f142e48886cc82eb879d37a3e7203b06cea75aa32d","leaf_index":223906,"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":"310624c26e20307043a57dd655ef11782ff8377f88afbb0ff76bbece42180299","side":"right"},{"sibling":"029aa1365dd6c24bee6b8dce5e610afe9a4143d6e63154838c052512f8c72aaf","side":"left"},{"sibling":"ed23084491c6ca4a270ef5aea33624308bc224feddcd5584547c3d45e072b2c4","side":"right"},{"sibling":"df034d66b9f3b226ce14dc6ee024e0fac3787b06bff90766541988492a93f9f5","side":"right"},{"sibling":"eeb2c6e755f237af2f26807da893a29350438af5d9755bce3d141c207686ed8e","side":"right"},{"sibling":"492736a124b586f23aca170f048f659dda7232be55f1439d49798fc4fb2c4455","side":"left"},{"sibling":"d9e96a026bf19228243264aa70a028a48f8a58ae04caab8ebd434847bf9e27ac","side":"right"},{"sibling":"e9e4595b6d3a8db8d409d92f766595bee2c79e9389fc033969243fd816d368c5","side":"left"},{"sibling":"fad4d9627e4b025e7840b4e896082fb8291cbf1a4c05653b3a789c8a4205d4b5","side":"right"},{"sibling":"e8dcea313a54920d83e4f72d5a4223f986c719f264241d171c4712efaaf1fc54","side":"left"},{"sibling":"5480e1ea31f4744f9bd7c4261771fe51f2cdb01e705cc17320bfc202d935ca12","side":"right"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","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":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","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_3698509c7fd05785c71c2cf2090deeffffef9bd5d13aa85b8a1d59c6ad0104ee"}}