Pith Number

pith:RDHSWXEJ

pith:2026:RDHSWXEJUSEVADPSHFSOBHRG33

not attested not anchored not stored refs resolved

ViT-K: A Few-Shot Learning Model for Coupled Fluid-Porous Media Flows with Interface Conditions

Changxin Qiu, Menghui Xu, Mengjia Chen, Zhiping Mao

ViT-K learns stable long-term predictions for coupled fluid-porous flows from few examples by linearizing dynamics with a Koopman operator.

arxiv:2605.13912 v1 · 2026-05-13 · math.NA · cs.NA · physics.flu-dyn

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Claims

C1strongest claim

By lifting nonlinear dynamics into a globally linear observable space, the ViT-K model provides stability by design, ensuring that prediction errors grow linearly rather than exponentially over time.

C2weakest assumption

That the Koopman operator can be learned effectively from sparse data to linearize the full coupled Stokes/Navier-Stokes-Darcy system including interface conditions without losing essential nonlinear physics or requiring extensive hyperparameter tuning.

C3one line summary

ViT-K uses Vision Transformers and Koopman operators to learn stable long-term spatiotemporal dynamics of coupled fluid-porous media flows from sparse data.

References

53 extracted · 53 resolved · 0 Pith anchors

[1] Advances in neural information processing systems , volume=

[2] Journal of Hydrology , volume= 2016

[3] Domain decomposition methods for the coupling of surface and groundwater flows , author=. 2004 , type= 2004

[4] Computational issues related to iterative coupling of subsurface and channel flows , author=. Calcolo , volume=. 2007 , publisher= 2007

[5] Transport in porous media , volume= 2006

Receipt and verification

First computed	2026-05-17T23:39:18.801424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88cf2b5c89a489500df23964e09e26defa900da65cf61028aaf6412ae5ed9653

Aliases

arxiv: 2605.13912 · arxiv_version: 2605.13912v1 · doi: 10.48550/arxiv.2605.13912 · pith_short_12: RDHSWXEJUSEV · pith_short_16: RDHSWXEJUSEVADPS · pith_short_8: RDHSWXEJ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/RDHSWXEJUSEVADPSHFSOBHRG33 \
  | 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: 88cf2b5c89a489500df23964e09e26defa900da65cf61028aaf6412ae5ed9653

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "2e27b288dfb0f1ebc78fe0167d647b1f1cc015b1275804a587eec12dcdb029a4",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T08:27:17Z",
    "title_canon_sha256": "38a52c4292a02e333ce0698a536996354c7cea96067294381ecc14b490ebd614"
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  "schema_version": "1.0",
  "source": {
    "id": "2605.13912",
    "kind": "arxiv",
    "version": 1
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}