Pith Number

pith:HG6IZUGS

pith:2026:HG6IZUGSFT5BA73UDPMEC6MJYY

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Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning

Benjamin Holzschuh, Felix Koehler, Nils Thuerey, Qiang Liu

Autoencoders pre-trained on single-channel spatial crops of synthetic 3D PDE data transfer to dynamics learning and generation across diverse physical systems.

arxiv:2605.15284 v1 · 2026-05-14 · cs.LG

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Record completeness

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Claims

C1strongest claim

Although pre-trained solely as an autoencoder on single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions and can be efficiently applied for multiple downstream tasks including dynamics learning via a novel parameter-efficient fine-tuning strategy.

C2weakest assumption

That representations learned by autoencoding single-channel spatial crops from online-generated synthetic 3D PDE data will transfer effectively to temporal dynamics modeling and generative tasks across different physical systems without requiring large amounts of task-specific data or architecture changes.

C3one line summary

Tadpole is a pre-trained autoencoder foundation model for 3D PDEs that learns transferable representations from online-generated data and supports efficient fine-tuning for dynamics prediction and other tasks.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] URL https://proceedings.mlr.press/ v235/chen24n.html. Cox, S. and Matthews, P. Exponential Time Dif- ferencing for Stiff Systems. Journal of Compu- tational Physics , 176(2):430–455, 2002. ISSN 0021-9 2002 · doi:10.1006/jcph.2002

[2] 2023 , month = mar, publisher = 2023 · doi:10.1038/s42256-023-00626-4

[3] doi: https://doi.org/10.1016/j.neucom.2021.04 2021 · doi:10.1016/j.neucom.2021.04

[4] Holzschuh, B., Liu, Q., Kohl, G., and Thuerey, N 2025

[5] URL https:// epubs.siam.org/doi/10.1137/24M1636071 2024 · doi:10.1137/24m1636071

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:50.619893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39bc8cd0d22cfa107f741bd8417989c6332121cbfa107fab6e3815d8ed17f91f

Aliases

arxiv: 2605.15284 · arxiv_version: 2605.15284v1 · doi: 10.48550/arxiv.2605.15284 · pith_short_12: HG6IZUGSFT5B · pith_short_16: HG6IZUGSFT5BA73U · pith_short_8: HG6IZUGS

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HG6IZUGSFT5BA73UDPMEC6MJYY \
  | 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: 39bc8cd0d22cfa107f741bd8417989c6332121cbfa107fab6e3815d8ed17f91f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0b29426463e6016b65e28b6c0164c4bd9e3746f853020d469bfe758bcd7ed75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T18:00:58Z",
    "title_canon_sha256": "4e04b9d4ace2e745657aa227e72f10f217718025de921d2d36881d080af5ccaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15284",
    "kind": "arxiv",
    "version": 1
  }
}