Pith Number

pith:75HRBPA7

pith:2026:75HRBPA7RL4ZYMC7JBVEOFFYG7

not attested not anchored not stored refs pending

Neural Preconditioned Born Series: A Metric-Matched Framework for Learning-based Preconditioners

Jiwei Jia, Juntao Wang, Xinliang Liu

Neural Preconditioned Born Series replaces the scalar Born correction with a learned map in residual coordinates induced by a constant-coefficient reference operator.

arxiv:2603.18527 v4 · 2026-03-19 · math.NA · cs.NA

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\pithnumber{75HRBPA7RL4ZYMC7JBVEOFFYG7}

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Record completeness

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Numerical results on heterogeneous Helmholtz benchmarks show that the metric-matched formulation consistently reduces iteration counts relative to direct residual learning and classical CBS, with stronger benefits in more ill-conditioned regimes.

C2weakest assumption

The equivalence between Born-series residuals and shifted-Laplacian left preconditioning holds for the chosen constant-coefficient references, and the learned residual-to-correction map generalizes from the training distribution to unseen heterogeneous media without degrading the iteration.

C3one line summary

NPBS learns a residual-to-correction map inside Born-series coordinates with a metric-matched objective, reducing iterations versus direct residual learning and classical CBS on heterogeneous Helmholtz benchmarks.

Receipt and verification

First computed	2026-05-20T00:00:36.856902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff4f10bc1f8af99c305f486a4714b837c11e30823c71e7fcd9d814c4bd4ac8ef

Aliases

arxiv: 2603.18527 · arxiv_version: 2603.18527v4 · doi: 10.48550/arxiv.2603.18527 · pith_short_12: 75HRBPA7RL4Z · pith_short_16: 75HRBPA7RL4ZYMC7 · pith_short_8: 75HRBPA7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/75HRBPA7RL4ZYMC7JBVEOFFYG7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ff4f10bc1f8af99c305f486a4714b837c11e30823c71e7fcd9d814c4bd4ac8ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a49cb4dcb0fd0c623dc60313ccc758b245469d086f14c9a1480c1ca08b5c0f6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-03-19T06:17:20Z",
    "title_canon_sha256": "bee462fb290bbf89efab04f643ff75d590e932d2b192bf75666431bd7e33bdfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.18527",
    "kind": "arxiv",
    "version": 4
  }
}