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This gap motivates our central question of whether neural networks can learn or select globally conserved quantities from physical trajectories. We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass. We use a structured $T(v)+V(q)$ energy model, a black-box Conservation Discovery Network (CDN), a polynomial CDN, and a conditional diffusion baseline. The structured network reaches $R^2 \\geq 0.9999$ against analytical energy on clean data, while the black-box CDN reaches $R^2 \\geq 0.996$ when trained with temporal consistency plus a small alignment loss to analytical energy at $t=0$ ($\\lambda_{\\mathrm{align}}=0.2$","title":"Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators","url":"https://arxiv.org/abs/2605.18883","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.18883v1 Announce Type: cross \nAbstract: A diffusion model trained on Hamiltonian trajectories can achieve rollout MSE near $10^{-3}$, but the standard deviation of its energy over time is between 7500 and 36000 times larger than the ground-truth energy standard deviation, indicating a failure to preserve conservation laws. This gap motivates our central question of whether neural networks can learn or select globally conserved quantities from physical trajectories. We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass. We use a structured $T(v)+V(q)$ energy model, a black-box Conservation Discovery Network (CDN), a polynomial CDN, and a conditional diffusion baseline. The structured network reaches $R^2 \\geq 0.9999$ against analytical energy on clean data, while the black-box CDN reaches $R^2 \\geq 0.996$ when trained with temporal consistency plus a small alignment loss to analytical energy at $t=0$ ($\\lambda_{\\mathrm{align}}=0.2$","title":"Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.18883"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:43f8e6fddb404e1052ac5374c0c5b0b55e6331fcd93e47cae94f5d1e352f73de789c992b11e85d7f8b9bc97e97edd4093bc356fe4753feeb2e56e583b75a3404","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.18883"},"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":"b55616a0081b13049a9ba85eb6d461534c3db5370b13d440ba0884044f501d85","leaf_index":145035,"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":"95988764aee2d1181aad660ba60f26191ea281afeb51bf0d1b22f09cc6fa2d3d","side":"left"},{"sibling":"bb0008e85cca906cc45b88ef664949df819918705548cd11e008ce34b430e15b","side":"left"},{"sibling":"67578dea13be0561586522179221d37d86a230d622484dc84b8d8b8fe587bcaf","side":"right"},{"sibling":"361ee222d2362a8c044f1a0de2899cc2df420c8b70a5995e49f2259eddf52187","side":"left"},{"sibling":"148b11a5ac76a6dd703868823dfa462ac7e41cdc1a5aada9ce2c9a103eb39f09","side":"right"},{"sibling":"0ab1cbf9ea1c7bc2998254a1b9ed1ffec18ac6f82d1467ebc2dcb67301c9ac1e","side":"right"},{"sibling":"3c054fc9610e75398c84d6602026026e93d4cc85db18f6da86b0e99184718c59","side":"right"},{"sibling":"3047d0cbdc103ff93a1a073ea940e12ff062595dae419513748ed63fbcb3359c","side":"left"},{"sibling":"9db04d2181fb869f16a5baf7dcfe999cc93a7e9beef8493d0cc71f57470fe5e1","side":"right"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"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":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","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_dbed965c22e6d1a5776db33db0fd9e62756249486b22ae46bbea40ba45dfde79"}}