Pith Number

pith:SWB5FQXR

pith:2026:SWB5FQXRHVCWF2KMOTWVQQJ2M5

not attested not anchored not stored refs pending

Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting

Carlos A. Pereira, Christopher Subich, David Millard, Eldad Haber, Emilia Diaconescu, Raymond J. Spiteri, Sasa Zhang, Shoyon Panday, Siddharth Rout, Siqi Wei, St\'ephane Gaudreault, Valentin Dallerit

A neural semi-Lagrangian architecture decomposes weather forecasting into advection, diffusion, and reaction blocks on latent variables.

arxiv:2601.21151 v2 · 2026-01-29 · cs.LG · physics.ao-ph

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4 Citations 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

Evaluated on ERA5 benchmarks, PARADIS achieves competitive deterministic forecast skill, with particularly strong short-lead performance, while preserving substantially better spectral fidelity and forecast activity during medium-range rollouts.

C2weakest assumption

That imposing a functional decomposition into advection, diffusion-like mixing, and reaction blocks on latent variables will produce physically meaningful trajectories and superior spectral properties without introducing artifacts from the differentiable interpolation or learned latent modes.

C3one line summary

PARADIS decomposes weather dynamics into advection via differentiable Neural Semi-Lagrangian transport, depthwise-separable diffusion, and pointwise reaction terms, yielding competitive ERA5 forecasts with improved spectral fidelity in medium-range rollouts.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Examining Fast Radiatively Driven Responses Using Machine-Learning Weather Emulators

Receipt and verification

First computed	2026-05-17T23:39:00.132566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9583d2c2f13d4562e94c74ed58413a6756872df72a098823c3a8f897f2f72b7e

Aliases

arxiv: 2601.21151 · arxiv_version: 2601.21151v2 · doi: 10.48550/arxiv.2601.21151 · pith_short_12: SWB5FQXRHVCW · pith_short_16: SWB5FQXRHVCWF2KM · pith_short_8: SWB5FQXR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SWB5FQXRHVCWF2KMOTWVQQJ2M5 \
  | 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: 9583d2c2f13d4562e94c74ed58413a6756872df72a098823c3a8f897f2f72b7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c40bc4c22dc18a2fdaa93ff68ff4a39ab452e94d7fdb64a6e5940c857f12540a",
    "cross_cats_sorted": [
      "physics.ao-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-29T01:20:21Z",
    "title_canon_sha256": "338e8da8bdd05c2d9223de3b819fb43f2da643920da08633de9467567f6c7503"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.21151",
    "kind": "arxiv",
    "version": 2
  }
}