Pith Number

pith:ZVO3SCT4

pith:2026:ZVO3SCT4PGMIPKW3W5TOTDQMC2

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Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

Huanhuan Gao, Zhangyong Liang

Augmenting low-regularity integrators with scaled neural corrections yields global error C(ε_net + δ) τ^γ ln(1/τ) for nonlinear dispersive equations.

arxiv:2605.04853 v2 · 2026-05-06 · cs.LG

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\pithnumber{ZVO3SCT4PGMIPKW3W5TOTDQMC2}

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Claims

C1strongest claim

Under stated assumptions, the global error satisfies C(ε_net + δ) τ^γ ln(1/τ); experiments on three dispersive benchmarks with rough data show improved accuracy over analytical integrators, splitting methods, and neural PDE surrogates, with stable spatial refinement and out-of-distribution transfer.

C2weakest assumption

The neural correction's Lipschitz contribution remains O(τ) after explicit time-step scaling, and the network approximation quality ε_net plus training shortfall δ are small enough for the Gronwall factor to stay bounded independently of spatial resolution.

C3one line summary

A hybrid solver-neural framework achieves global error O(τ^γ ln(1/τ)) for nonlinear dispersive equations by training a lightweight network on the residual defect inside the solver loop while preserving uniform stability.

Receipt and verification

First computed	2026-06-11T01:09:37.065467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd5db90a7c799887aadbb766e98e0c1696f045764028b336e4c714c60effc62b

Aliases

arxiv: 2605.04853 · arxiv_version: 2605.04853v2 · doi: 10.48550/arxiv.2605.04853 · pith_short_12: ZVO3SCT4PGMI · pith_short_16: ZVO3SCT4PGMIPKW3 · pith_short_8: ZVO3SCT4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZVO3SCT4PGMIPKW3W5TOTDQMC2 \
  | 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: cd5db90a7c799887aadbb766e98e0c1696f045764028b336e4c714c60effc62b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d49fb045488786fb58b0028fbf6e995db1da1fd05800c49c2fd86dce49c10124",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-06T12:50:36Z",
    "title_canon_sha256": "110ebae5ea646da47a76b28b7776637e230af8f8ac55580f725fa289a644cc8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04853",
    "kind": "arxiv",
    "version": 2
  }
}