Pith Number

pith:OPKNYLPQ

pith:2026:OPKNYLPQEM6DRKVWIF24URMZTL

not attested not anchored not stored refs pending

An Energy Stable Approach for Learning Derivative Operators from Noisy Data for Maxwells Equations

Ameh Emmanuel Sunday, Victory C. Obieke

Reduced parameterization lets SP-ADMM learn energy-conserving derivative operators for Maxwell equations directly from noisy data.

arxiv:2601.01902 v7 · 2026-01-05 · math.NA · cs.NA

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\pithnumber{OPKNYLPQEM6DRKVWIF24URMZTL}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

SP-ADMM achieves the smallest final-time electric-field error while preserving energy to roundoff accuracy across clean data, noisy derivative data, multiple initial conditions, different hidden skew-adjoint operators, training-set sizes, regularization parameters, constraint ablations, and long-time simulations.

C2weakest assumption

That enforcing skew-adjointness solely through reduced parameterization of the positive-side stencil coefficients is sufficient to guarantee energy stability for the learned operator in the underlying Maxwell system without introducing approximation errors or limiting expressivity.

C3one line summary

SP-ADMM learns energy-stable derivative stencils for Maxwell equations from noisy data by enforcing skew-adjointness through reduced parameterization of periodic convolution stencils.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-08T01:03:54.647621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73d4dc2df0233c38aab64175ca45999af4593d84072febedc8462fae7a219d06

Aliases

arxiv: 2601.01902 · arxiv_version: 2601.01902v7 · doi: 10.48550/arxiv.2601.01902 · pith_short_12: OPKNYLPQEM6D · pith_short_16: OPKNYLPQEM6DRKVW · pith_short_8: OPKNYLPQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OPKNYLPQEM6DRKVWIF24URMZTL \
  | 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: 73d4dc2df0233c38aab64175ca45999af4593d84072febedc8462fae7a219d06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14094ab75bf335d9892b47a2cdcbd03e9c63375be8eccaa79c93d6e63aa9acd4",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-01-05T08:46:15Z",
    "title_canon_sha256": "e5ab3d45af06a64cb5426529a4af139f76f3b3d8da8cf9eaad596dd4c3387d2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.01902",
    "kind": "arxiv",
    "version": 7
  }
}