Pith Number

pith:CUQJZBOA

pith:2026:CUQJZBOAJXULVTZ24N6YEKF3GC

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fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations

Binghang Lu, Christian Moya, Guang Lin, Zhaopeng Hao

The fPINN-DeepONet framework solves multi-term time-fractional mixed diffusion-wave equations with variable fractional orders by combining operator learning and an L2 approximation for Caputo derivatives.

arxiv:2605.16594 v1 · 2026-05-15 · math.NA · cs.LG · cs.NA

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Claims

C1strongest claim

The fPINN-DeepONet framework efficiently solves multi-term time-fractional mixed diffusion-wave equations with dynamically varying fractional orders in both space and time while remaining accurate and robust even with noisy data.

C2weakest assumption

The derived L2 approximation achieves first-order accuracy for the Caputo fractional derivative of order β ∈ (1,2) and can be directly integrated into the operator learning architecture without loss of stability or consistency.

C3one line summary

fPINN-DeepONet integrates an L2 approximation for the Caputo derivative with DeepONet to solve multi-term time-fractional PDEs, including cases with space-time varying orders and noisy data.

References

35 extracted · 35 resolved · 5 Pith anchors

[1] Finite difference schemes for multi-term time-fractional mixed diffusion-wave equations 2016 · arXiv:1607.07104

[2] J. F. Kelly, R. J. McGough, M. M. Meerschaert, Analytical time-domain Green’s functions for power-law media, J. Acoust. Soc. Am. 124 (5) (2008) 2861-2872 2008

[3] J. Chen, F. Liu, V. Anh, S. Shen, Q. Liu, C. Liao, The analytical solution and numerical solution of the fractional diffusion-wave equation with damping, Appl. Math. Comput. 219 (2012) 1737-1748 2012

[4] R. Schumer, D. A. Benson, M. M. Meerschaert, B. Baeumer, Fractal mobile/immobile solute transport, Water Res. Research. 39 (10) (2003) 1296 2003

[5] R. Metzler, J. Klafter, I. M. Sokolov, Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended, Phys. Rev. E 58 (2) (1998) 1621-1633 1998

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:31.644457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15209c85c04de8bacf3ae37d8228bb30ae5701966612aa59c3100aff0eb01b27

Aliases

arxiv: 2605.16594 · arxiv_version: 2605.16594v1 · doi: 10.48550/arxiv.2605.16594 · pith_short_12: CUQJZBOAJXUL · pith_short_16: CUQJZBOAJXULVTZ2 · pith_short_8: CUQJZBOA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CUQJZBOAJXULVTZ24N6YEKF3GC \
  | 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: 15209c85c04de8bacf3ae37d8228bb30ae5701966612aa59c3100aff0eb01b27

Canonical record JSON

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    "abstract_canon_sha256": "85b353fae7834799b32569bd2cfcffe34e07a578e3f43029f8d68728843af8b4",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-15T19:57:17Z",
    "title_canon_sha256": "3729a31296e8d6499a5b577348044dfed7668e10342142e63b314767b7cf0c6c"
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    "kind": "arxiv",
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