Pith Number

pith:PLEFZJW5

pith:2026:PLEFZJW5EZOVHL5EVSDJAKTIYX

not attested not anchored not stored refs resolved

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs

Guofeng Su, Hongxiang Ma, Lang Qin, Rui Yang, Shan Ding, Yongfu Tian

Encoding spatial and temporal information via separate subnetworks allows a physics-informed neural operator to avoid error accumulation in long-time predictions of parametric PDEs.

arxiv:2605.15754 v1 · 2026-05-15 · physics.comp-ph · cs.CE

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLEFZJW5EZOVHL5EVSDJAKTIYX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Claims

C1strongest claim

By encoding spatial and temporal information via two separate subnetworks, the PI-SWNO framework structurally mitigates the accumulation of errors over extended time intervals while the time-marching batch-wise sampling resolves the memory bottleneck.

C2weakest assumption

The decoupling paradigm that combines time-invariant spatial basis functions with time-varying evolution coefficients will prevent error accumulation for the target class of time-dependent parametric PDEs, as grounded in the Stone-Weierstrass approximation theorem.

C3one line summary

A spatiotemporally decoupled physics-informed Stone-Weierstrass neural operator for stable long-time prediction of time-dependent parametric PDEs.

References

41 extracted · 41 resolved · 5 Pith anchors

[1] A. M. Vargas, Finite difference method for solving fractional differential equations at irregular meshes, Mathematics and Computers in Simulation 193 (2022) 204–216.doi:https: //doi.org/10.1016/j.matc 2022 · doi:10.1016/j.matcom.2021.10.010

[2] K. Kergrene, I. Babuška, U. Banerjee, Stable generalized finite element method and associated iterative schemes; application to interface prob- lems, Computer Methods in Applied Mechanics and Engineer 2016 · doi:10.1016/j.cma.2016.02.030

[3] P. Buchmüller, J. Dreher, C. Helzel, Finite volume weno methods for hyperbolic conservation laws on cartesian grids with adaptive mesh refinement, Applied Mathematics and Computation 272 (2016) 460–47 2016 · doi:10.1016/j.amc.2015.03.078

[4] M. Raissi, P. Perdikaris, G. Karniadakis, Physics-informed neu- ral networks: A deep learning framework for solving forward 60 and inverse problems involving nonlinear partial differential equa- tions 2019 · doi:10.1016/j.jcp.2018.10.045

[5] Z. Li, K. Meidani, A. B. Farimani, Transformer for partial differen- tial equations’ operator learning, Transactions on Machine Learning Re- search (2023). URLhttps://openreview.net/forum?id=EPPqt3uER 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:16.440830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ac85ca6dd265d53afa4ac86902a68c5fe1950f009c15521203584b78d6af245

Aliases

arxiv: 2605.15754 · arxiv_version: 2605.15754v1 · doi: 10.48550/arxiv.2605.15754 · pith_short_12: PLEFZJW5EZOV · pith_short_16: PLEFZJW5EZOVHL5E · pith_short_8: PLEFZJW5

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/PLEFZJW5EZOVHL5EVSDJAKTIYX \
  | 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: 7ac85ca6dd265d53afa4ac86902a68c5fe1950f009c15521203584b78d6af245

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "056ab8f50256124dfa775e8bc3270d1e9a422e6d9fe7c063eff5fe45fa153117",
    "cross_cats_sorted": [
      "cs.CE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2026-05-15T09:15:01Z",
    "title_canon_sha256": "6525041d00ee4efb6aa1670605574ce932ef6cf6161cef0cebd03eecd9945650"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15754",
    "kind": "arxiv",
    "version": 1
  }
}