Pith Number

pith:6RVJNHUX

pith:2026:6RVJNHUXYIABNE2ICTL7JUBIMN

not attested not anchored not stored refs resolved

Imposing Boundary Conditions on Neural Operators via Learned Function Extensions

Laura De Lorenzis, Sepehr Mousavi, Siddhartha Mishra

Mapping boundary data to full-domain latent extensions lets any standard neural operator handle complex mixed-type conditions accurately.

arxiv:2602.04923 v2 · 2026-02-04 · cs.LG

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\pithnumber{6RVJNHUXYIABNE2ICTL7JUBIMN}

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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

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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

Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets.

C2weakest assumption

That mapping boundary data to learned latent pseudo-extensions defined over the entire domain will allow any standard neural operator to capture rich dependencies on complex, mixed-type, and multi-segment BCs without introducing artifacts or requiring architecture-specific changes.

C3one line summary

A framework learns boundary-to-domain pseudo-extensions to condition neural operators on complex BCs, achieving SOTA accuracy on 18 challenging PDE datasets without hyperparameter tuning.

References

37 extracted · 37 resolved · 3 Pith anchors

[1] B. Alkin, A. Fürst, S. Schmid, L. Gruber, M. Holzleitner, and J. Brandstetter. Universal physics transformers: A framework for efficiently scaling neural operators. In A. Globerson, L. Mackey, D. Belg 2024

[3] Layer Normalization 2016 · arXiv:1607.06450

[4] I. A. Baratta, J. P. Dean, J. S. Dokken, M. Habera, J. S. Hale, C. N. Richardson, M. E. Rognes, M. W. Scroggs, N. Sime, and G. N. Wells. DOLFINx: the next generation FEniCS problem solving environment 2023

[5] F. Bartolucci, E. de Bezenac, B. Raonic, R. Molinaro, S. Mishra, and R. Alaifari. Representation equivalent neural operators: a framework for alias-free operator learning.Advances in Neural Informatio 2023

[6] J. Brandstetter, D. E. Worrall, and M. Welling. Message passing neural PDE solvers. InInternational Conference on Learning Representations, 2022 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:45:05.487361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f46a969e97c20016934814d7f4d028637fe8ee4312c1e2827a7b6cd0ce3d4513

Aliases

arxiv: 2602.04923 · arxiv_version: 2602.04923v2 · doi: 10.48550/arxiv.2602.04923 · pith_short_12: 6RVJNHUXYIAB · pith_short_16: 6RVJNHUXYIABNE2I · pith_short_8: 6RVJNHUX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6RVJNHUXYIABNE2ICTL7JUBIMN \
  | 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: f46a969e97c20016934814d7f4d028637fe8ee4312c1e2827a7b6cd0ce3d4513

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48580172f9e69804c2734be99280e589e6447be3292689002d27bd966aac313e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-02-04T08:28:43Z",
    "title_canon_sha256": "5fc153438a6e3d6649ae0a638f690109c29916e3bfe71c3ae9bc2a7b6f7f05a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.04923",
    "kind": "arxiv",
    "version": 2
  }
}