Pith Number

pith:EG4GTHST

pith:2026:EG4GTHSTGSCZQ2IHRRJWOM7JXQ

not attested not anchored not stored refs resolved

U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics

Jinliang Liu, Xiao Yang, Yingzhe Ma, Yuxin Xie, Zihan Xiong

U-HNO uses per-point hard masks to route between global Fourier and local Gaussian branches for PDEs with mixed smooth and sharp dynamics.

arxiv:2605.12965 v1 · 2026-05-13 · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EG4GTHSTGSCZQ2IHRRJWOM7JXQ}

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

Across benchmarks spanning 1D Burgers, Kuramoto-Sivashinsky, KdV, 2D advection, Allen-Cahn, Navier-Stokes, Darcy flow, and 3D transonic compressible Navier-Stokes from PDEBench, U-HNO achieves state-of-the-art rollout accuracy on the majority of tasks in both relative L^2 and H^1 metrics, with the largest gains on problems dominated by sharp localized features.

C2weakest assumption

The assumption that a per-pixel hard mask based on local contrast of the routing signal can reliably select the appropriate branch (global or local) without causing training instabilities or degrading performance on smooth regions, and that this adaptive mixture generalizes across different PDE types.

C3one line summary

U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.

References

30 extracted · 30 resolved · 5 Pith anchors

[1] Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation 2013 · arXiv:1308.3432

[2] Spherical fourier neural operators: Learning stable 9 dynamics on the sphere 2023

[3] Message passing neural pde solvers 2022

[4] Choose a transformer: Fourier or galerkin.Advances in neural information processing systems, 34:24924–24940, 2021 2021

[5] Gupta, G., Xiao, X., and Bogdan, P 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:09.084716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21b8699e5334859869078c536733e9bc3a89714de72d71d376629b6bde5e477f

Aliases

arxiv: 2605.12965 · arxiv_version: 2605.12965v1 · doi: 10.48550/arxiv.2605.12965 · pith_short_12: EG4GTHSTGSCZ · pith_short_16: EG4GTHSTGSCZQ2IH · pith_short_8: EG4GTHST

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/EG4GTHSTGSCZQ2IHRRJWOM7JXQ \
  | 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: 21b8699e5334859869078c536733e9bc3a89714de72d71d376629b6bde5e477f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66c0697cc472b32f2751225babb1cc94c1a9c51ec9da27c49212c9605f070554",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T04:00:43Z",
    "title_canon_sha256": "39b5b4a2b1867aa3754932f846586578ffd617276704c55e0f1c26dfd4c03755"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12965",
    "kind": "arxiv",
    "version": 1
  }
}