Pith Number

pith:JM46SQSF

pith:2020:JM46SQSF2XGDUIUKQS5M22VGEJ

not attested not anchored not stored refs pending

On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

George Em Karniadakis, Jerome Darbon, Yeonjong Shin

arxiv:2004.01806 v2 · 2020-04-03 · math.NA · cs.LG · cs.NA

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\usepackage{pith}
\pithnumber{JM46SQSF2XGDUIUKQS5M22VGEJ}

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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

8 papers in Pith

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks

Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions

Universal Approximation of Nonlinear Operators and Their Derivatives

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces

Receipt and verification

First computed	2026-07-05T02:02:33.561426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b39e94245d5cc3a228a84bacd6aa622485b8793564fd9b6e48ab1a5420b5830

Aliases

arxiv: 2004.01806 · arxiv_version: 2004.01806v2 · doi: 10.48550/arxiv.2004.01806 · pith_short_12: JM46SQSF2XGD · pith_short_16: JM46SQSF2XGDUIUK · pith_short_8: JM46SQSF

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/JM46SQSF2XGDUIUKQS5M22VGEJ \
  | 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: 4b39e94245d5cc3a228a84bacd6aa622485b8793564fd9b6e48ab1a5420b5830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0559631af684ebbe1464d53cba980d890e9c40fb73a203b7f3a746d752da9f7",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2020-04-03T22:59:25Z",
    "title_canon_sha256": "a3d3a9eedee973cf152566b885811a0830f4818e583b5e71a315b20227cbdaa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.01806",
    "kind": "arxiv",
    "version": 2
  }
}