Pith Number

pith:CFBEFQVR

pith:2026:CFBEFQVR2YZK6TYQGMBVT7XL4L

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A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributions

Chengli Tan, Jing Feng, Qi Liu, Xiaolong Wang, Yong Xu, Yuanyuan Liu

A single deep learning model solves transient Fokker-Planck equations for arbitrary initial distributions, parameters, and times after one training.

arxiv:2604.06001 v2 · 2026-04-07 · physics.comp-ph · cs.LG

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\usepackage{pith}
\pithnumber{CFBEFQVR2YZK6TYQGMBVT7XL4L}

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Record completeness

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3 Author claim open · sign in to claim

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

via a single training process, simultaneously resolves transient FPE solutions for arbitrary multi-modal initial distributions, system parameters, and time points.

C2weakest assumption

That Gaussian mixture distributions plus a bijective constraint-preserving autoencoder can faithfully represent and evolve the full range of initial, transient, and stationary distributions for the target systems without loss of accuracy or generalization failure outside the training distribution.

C3one line summary

A constraint-preserving autoencoder maps Gaussian mixture parameters to latent space where a single evolution network models transient dynamics across arbitrary initial conditions and system parameters for the Fokker-Planck equation.

Receipt and verification

First computed	2026-06-19T16:12:20.075302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

114242c2b1d632af4f10330359feebe2ee42bad6b4d1e38d28b25c9e0fd1a5b0

Aliases

arxiv: 2604.06001 · arxiv_version: 2604.06001v2 · doi: 10.48550/arxiv.2604.06001 · pith_short_12: CFBEFQVR2YZK · pith_short_16: CFBEFQVR2YZK6TYQ · pith_short_8: CFBEFQVR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CFBEFQVR2YZK6TYQGMBVT7XL4L \
  | 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: 114242c2b1d632af4f10330359feebe2ee42bad6b4d1e38d28b25c9e0fd1a5b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8973bd89f2cec50ef481b1b9080fc7569b77eff27b6f18a844a6187448b09328",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2026-04-07T15:28:53Z",
    "title_canon_sha256": "8cb670409c7c544f24449dab72f255f13038d029240482fe8cee712c339fe89c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06001",
    "kind": "arxiv",
    "version": 2
  }
}