Pith Number

pith:T6J5L633

pith:2024:T6J5L633U5DA54GMGBZRZGDLVL

not attested not anchored not stored refs pending

An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning

Adrian Riekert, Arnulf Jentzen, Benno Kuckuck, Lukas Gonon, Philippe von Wurstemberger, Siyu Liang

arxiv:2408.13222 v1 · 2024-08-23 · math.NA · cs.NA · stat.ML

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T6J5L633U5DA54GMGBZRZGDLVL}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

Random Neural Network Expressivity for Non-Linear Partial Differential Equations

Receipt and verification

First computed	2026-07-05T08:58:37.220767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f93d5fb7ba7460ef0cc30731c986baad5c5faaecc65f4df0d9166af75520e76

Aliases

arxiv: 2408.13222 · arxiv_version: 2408.13222v1 · doi: 10.48550/arxiv.2408.13222 · pith_short_12: T6J5L633U5DA · pith_short_16: T6J5L633U5DA54GM · pith_short_8: T6J5L633

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T6J5L633U5DA54GMGBZRZGDLVL \
  | 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: 9f93d5fb7ba7460ef0cc30731c986baad5c5faaecc65f4df0d9166af75520e76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "636e2e74d6bbfbcb009cc10dac2f6197e5ab870538be12c6291bc9430dd1efc2",
    "cross_cats_sorted": [
      "cs.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-08-23T16:57:34Z",
    "title_canon_sha256": "12353b4ca2c6ea027be35e0b44d0ed816f06a629df5decae8883b8a0436009f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.13222",
    "kind": "arxiv",
    "version": 1
  }
}