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While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose \\textsc{NPSolver}, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of relying on fully converged numerical solutions or raw PDE residuals, \\textsc{NPSolver} utilizes a small number of preconditioned conjugate gradient (PCG) steps to refine its own predictions, providing a more stable and well-scaled training signal. Theoretical analysis confirms that this iterative supervision serves as a well-conditioned error proxy and that a stop-gradient design is essential for o","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","url":"https://arxiv.org/abs/2605.25786","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.25786v1 Announce Type: cross \nAbstract: Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose \\textsc{NPSolver}, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of relying on fully converged numerical solutions or raw PDE residuals, \\textsc{NPSolver} utilizes a small number of preconditioned conjugate gradient (PCG) steps to refine its own predictions, providing a more stable and well-scaled training signal. Theoretical analysis confirms that this iterative supervision serves as a well-conditioned error proxy and that a stop-gradient design is essential for o","title":"NPSolver: Neural Poisson Solver with Iterative Physics Supervision","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-26T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.25786"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:5bc835fb00e7961c489a5e6cd1a17704177f5f4e28dab71204c77a2bc6252de94a5901d1555474c29b739649ac073d3f4f4d4ca75e1d09c41f6980f0eef61404","signer":"crovia.substrate","subject":{"observed_at":"2026-05-26T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.25786"},"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":"84d8382d7a39b845f9fd6862b60f9396b10a0d16c1d01537f8c4639f2088c0f6","leaf_index":151725,"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":"8b4498418f75a35ea1933735ddf565f5399c3d84a369ae72d23e678928e86e81","side":"left"},{"sibling":"89dacca31ba4330ffc54c492ce8b4c744d3b39d7298a21e3bfdfb53cc01ae236","side":"right"},{"sibling":"3dd558afeb03522f369d570d27ae6b59e168f7a7e1e8a498ff42bebe56c35c65","side":"left"},{"sibling":"d3e42249ee3fd632a08f1ceff531848a41e20504d5bc26c899f20850a583481d","side":"left"},{"sibling":"407b891d3da12cf74fa40ce1962a4cfd5e65de5213e830cf0164f8a665da6161","side":"right"},{"sibling":"1fdb62cc53d97a7f7a1438e1d514a795206e3fd636e208e00b18fba2519cd611","side":"left"},{"sibling":"59c025ecd2dec1777c83a364f63a0af602c1b8c1069e8b09513a2e68a6f64e32","side":"right"},{"sibling":"f9db7ff3c5db7011b2738b446bad7b165ec8fd162c800ba3bad08298201edaa3","side":"left"},{"sibling":"aff657821100efc777fe98abc63d25a13c2d813d2a00f85a278e295ee3a166b3","side":"right"},{"sibling":"879666fab72e779ab55d0564eaabd64b00534fd6bba7f18412c7f31f61ffd09f","side":"right"},{"sibling":"f40ccedd90c323817e961adc0a2e2db82b8aabe192b6c9d5a373ff988987b207","side":"right"},{"sibling":"b85ea61ae405eed84392a7b6b1eee5536f5a38d6b04070638e23ec7b71e3443a","side":"right"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"e5893793e3591ed7f5e58ca94ffcfba46bb30f69fb1c25d5ba8ef49eb99f9126","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e3eecaf996dbe7229a7bb1d234c97aea97a252c5f7c89f8547b6d091db0f0e40","side":"right"},{"sibling":"55bcbd4da3e20d93931f7e58673f10232e81a5b1514d7396cb4b71e8f95788d0","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":152106,"merkle_root":"ac5182c6f3dd09931f2a689df5f4be36df7b55e55bcf106e195671f5ed55fd8f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260526T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-26T05:37:34Z","sig_algorithm":"ed25519","signature":"a401243fbd2c077d29a623c6ef616c78fbd5c8ce1930afa7af7165b2386e5a8cf15d5094983a1c962e71b27b911a3f3ce09c8cfab9393be2ce5ce8ee6513da06","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_c5bb9722d9a555795389dff74e2761893389e88a13c6a29ea4d5d7aad82c302b"}}