Pith Number

pith:25JQ5POQ

pith:2026:25JQ5POQ46MNAGCJTHCHMVILMV

not attested not anchored not stored refs resolved

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

Takaharu Yaguchi, Takashi Matsubara, Yeang Makara, Yusuke Tanaka

Symplectic neural operators preserve structure to guarantee long-term stability in infinite-dimensional Hamiltonian systems.

arxiv:2605.15881 v1 · 2026-05-15 · math.DS · cs.AI · physics.comp-ph

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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

We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy.

C2weakest assumption

The learned operator must approximate the true dynamics with sufficient accuracy in addition to preserving symplecticity for the long-term stability result to hold in practice.

C3one line summary

Symplectic Neural Operators preserve symplectic structure for learning infinite-dimensional Hamiltonian PDEs and deliver improved long-term energy stability in theory and experiments.

References

35 extracted · 35 resolved · 3 Pith anchors

[1] Neural Networks , volume = 1989

[2] IEEE Transactions on Neural Networks , volume = 1995

[3] DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators 1910 · doi:10.48550/arxiv.1910.03193

[4] Nature Machine Intelligence , volume = 2021

[5] Neural Operator: Graph Kernel Network for Partial Differential Equations 2003 · doi:10.48550/arxiv.2003.03485

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:23.434387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7530ebdd0e798d0184999c476550b657bdaea47ea2dfa312e81a394d1677efd

Aliases

arxiv: 2605.15881 · arxiv_version: 2605.15881v1 · doi: 10.48550/arxiv.2605.15881 · pith_short_12: 25JQ5POQ46MN · pith_short_16: 25JQ5POQ46MNAGCJ · pith_short_8: 25JQ5POQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/25JQ5POQ46MNAGCJTHCHMVILMV \
  | 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: d7530ebdd0e798d0184999c476550b657bdaea47ea2dfa312e81a394d1677efd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a53d9ab972d05c6c95cb82df04211ba1a686b2aa8fee112517645009be35d82",
    "cross_cats_sorted": [
      "cs.AI",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T11:58:15Z",
    "title_canon_sha256": "df6be4044fab410f1205af66f1b279719a66bc092680df80382854979bdc7290"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15881",
    "kind": "arxiv",
    "version": 1
  }
}