Pith Number

pith:DVEKH3HK

pith:2026:DVEKH3HK72TPD3TGNAWSK4PTKB

not attested not anchored not stored refs pending

Hard-constrained Physics-informed Neural Networks for Interface Problems

Michael S. Penwarden, Pratanu Roy, Seung Whan Chung, Stephen T. Castonguay, Sumanta Roy, Yucheng Fu

Hard-constrained PINN formulations embed interface continuity and flux conditions directly into the neural network solution representation.

arxiv:2604.08453 v2 · 2026-04-09 · math.NA · cs.NA · physics.comp-ph

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Claims

C1strongest claim

We introduce two ansatz-based hard-constrained PINN formulations for interface problems that embed the interface physics into the solution representation and thereby decouple interface enforcement from PDE residual minimization.

C2weakest assumption

That the windowing construction remains stable for general interface geometries and that the discrete buffer correction points can be chosen without introducing new fitting parameters that affect accuracy.

C3one line summary

Hard-constrained PINN formulations via windowing and buffer approaches enforce interface conditions by design and outperform soft-constrained baselines on 1D and 2D elliptic interface problems.

Receipt and verification

First computed	2026-05-20T00:02:11.353662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d48a3eceafea6f1ee66682d2571f3507bbbca90f62b5b76cf49166b94a3d3dc

Aliases

arxiv: 2604.08453 · arxiv_version: 2604.08453v2 · doi: 10.48550/arxiv.2604.08453 · pith_short_12: DVEKH3HK72TP · pith_short_16: DVEKH3HK72TPD3TG · pith_short_8: DVEKH3HK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DVEKH3HK72TPD3TGNAWSK4PTKB \
  | 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: 1d48a3eceafea6f1ee66682d2571f3507bbbca90f62b5b76cf49166b94a3d3dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2965726b33b9ad8d3a2388fb75403578ce05707475198fc25d0b25308903570",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-09T16:49:55Z",
    "title_canon_sha256": "c6156e3b3572c1373c9702aa0d0968f355301b7bc8194517c2970de6079def09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08453",
    "kind": "arxiv",
    "version": 2
  }
}