Pith Number

pith:QCD73R43

pith:2026:QCD73R43WXACYNEKA5USXWRLU7

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Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks

Erik Burman, Jonatan Vallin, Karl Larsson, Mats G. Larson

Finite element spatial discretization paired with extreme learning machine parameter surrogates solves inverse parametrized PDE problems with explicit error estimates.

arxiv:2602.14757 v2 · 2026-02-16 · math.NA · cs.LG · cs.NA

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\pithnumber{QCD73R43WXACYNEKA5USXWRLU7}

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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

We establish existence, uniqueness, and regularity of the parametric solution and derive rigorous error estimates that explicitly quantify the interplay between spatial discretization and parameter approximation.

C2weakest assumption

In higher-dimensional parameter spaces, error bounds are obtained under explicit approximation and stability assumptions on the extreme learning machine surrogates.

C3one line summary

A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.

References

52 extracted · 52 resolved · 2 Pith anchors

[1] Alberti, Ángel Arroyo, and Matteo Santacesaria 2023 · doi:10.1088/1361-6544/aca73d

[2] Alberti and Matteo Santacesaria 2019 · doi:10.1017/fms.2019.31

[3] Alberti and Matteo Santacesaria 2022 · doi:10.1007/s00205-021-01718-4

[4] G. Alessandrini, M. V. de Hoop, F. Faucher, R. Gaburro, and E. Sincich. Inverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional well-posedness driven iterative reg 2019 · doi:10.1051/m2an/2019009

[5] Lipschitz stability for the inverse conductivity problem.Advances in Applied Mathematics, 35(2):207–241 2005 · doi:10.1016/j.aam.2004.12.002

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-04T01:08:45.498383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8087fdc79bb5c02c348a07692bda2ba7f4869f4aeacf1134b4cce420cdd9a4a1

Aliases

arxiv: 2602.14757 · arxiv_version: 2602.14757v2 · doi: 10.48550/arxiv.2602.14757 · pith_short_12: QCD73R43WXAC · pith_short_16: QCD73R43WXACYNEK · pith_short_8: QCD73R43

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QCD73R43WXACYNEKA5USXWRLU7 \
  | 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: 8087fdc79bb5c02c348a07692bda2ba7f4869f4aeacf1134b4cce420cdd9a4a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a458f8681d1173078d4841d6bd254ee348709fbdfb7cd9aead5e8e9eb9bd40e",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-02-16T14:01:50Z",
    "title_canon_sha256": "82a74826a6a70007e70532c57e5977d8f929e597690ac7369a798ac2fc5098a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.14757",
    "kind": "arxiv",
    "version": 2
  }
}