Pith Number

pith:CJP6YGLW

pith:2026:CJP6YGLWRI2YS7KZWOMM2BBMZC

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Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects

Boyi Zou, Gang Bao, Mingsheng Long, Yi Yang, Yuze Hao, Zhentao Tan

AI methods are reshaping inverse PDE problems by organizing them into unified categories of inference, design, and control.

arxiv:2605.16966 v1 · 2026-05-16 · cs.AI

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Claims

C1strongest claim

This survey aims to provide the first unified and systematic perspective on AI for inverse PDE problems, demonstrating how modern learning-based methods are reshaping inverse problems, inverse design, and control problems in PDE-governed systems.

C2weakest assumption

The assumption that the chosen methodological paradigms and representative state-of-the-art approaches from recent years, along with the three-category organization, sufficiently capture and structure the full breadth of advances in the field.

C3one line summary

A survey organizing AI methods for inverse PDE problems into inverse problems, inverse design, and control categories, covering applications and future challenges like physics-informed models and uncertainty quantification.

References

278 extracted · 278 resolved · 8 Pith anchors

[1] TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems 2016 · arXiv:1603.04467

[2] Robert Acar. 1993. Identification of the coefficient in elliptic equations.SIAM journal on control and optimization31, 5 (1993), 1221–1244 1993

[3] Gabriel Achour, Woong Je Sung, Olivia J Pinon-Fischer, and Dimitri N Mavris. 2020. Development of a conditional generative adversarial network for airfoil shape optimization. InAIAA Scitech 2020 Forum 2020

[4] Grégoire Allaire, François Jouve, and Anca-Maria Toader. 2004. Structural optimization using sensitivity analysis and a level-set method.Journal of computational physics194, 1 (2004), 363–393 2004

[5] Kelsey Allen, Tatiana Lopez-Guevara, Kimberly L Stachenfeld, Alvaro Sanchez Gonzalez, Peter Battaglia, Jessica B Hamrick, and Tobias Pfaff

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:33.451045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

125fec19768a35897d59b398cd042cc88ee17a0658fc0c665ccdf989d9731953

Aliases

arxiv: 2605.16966 · arxiv_version: 2605.16966v1 · doi: 10.48550/arxiv.2605.16966 · pith_short_12: CJP6YGLWRI2Y · pith_short_16: CJP6YGLWRI2YS7KZ · pith_short_8: CJP6YGLW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CJP6YGLWRI2YS7KZWOMM2BBMZC \
  | 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: 125fec19768a35897d59b398cd042cc88ee17a0658fc0c665ccdf989d9731953

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3aa843417a6454cdcf23c8c4ca4ba6713bc7885656780d45e3750c5adc860fdb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-16T12:41:36Z",
    "title_canon_sha256": "c42baf6b69628429fc79badf11c7be870d9a6335808543e8a7e1a84078e6674d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16966",
    "kind": "arxiv",
    "version": 1
  }
}