Pith Number

pith:KZZLOGEL

pith:2026:KZZLOGELSYXSP7X5CBSRB5IARD

not attested not anchored not stored refs resolved

MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Lake Yang, Serafim Kalliadasis

Combining a soft physics residual with multiple-initial-condition shooting lets Neural ODEs recover the true vector field from few trajectories.

arxiv:2605.13305 v1 · 2026-05-13 · cs.LG · math.DS · physics.chem-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZZLOGELSYXSP7X5CBSRB5IARD}

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

On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 26% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.

C2weakest assumption

That the soft physics-informed residual and MIC multiple-shooting curriculum are structurally complementary such that the physics term anchors the vector-field magnitude on the enlarged support created by MIC, leading to recovery of the underlying dynamics.

C3one line summary

MPINeuralODE combines soft physics residuals with multiple-initial-condition training to reduce out-of-sample and long-horizon errors in dynamical system learning.

References

30 extracted · 30 resolved · 2 Pith anchors

[1] Lotka , title =

[2] Nature , volume =

[3] L. S. Pontryagin and V. G. Boltyanskii and R. V. Gamkrelidze and E. F. Mishchenko , title =

[4] Murray , title =

[5] Strogatz , title =

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T02:44:48.972660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5672b7188b962f27fefd106510f50088d1dffef028b4c32520695b1e6e1a4cb2

Aliases

arxiv: 2605.13305 · arxiv_version: 2605.13305v1 · doi: 10.48550/arxiv.2605.13305 · pith_short_12: KZZLOGELSYXS · pith_short_16: KZZLOGELSYXSP7X5 · pith_short_8: KZZLOGEL

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/KZZLOGELSYXSP7X5CBSRB5IARD \
  | 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: 5672b7188b962f27fefd106510f50088d1dffef028b4c32520695b1e6e1a4cb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba80ced96078f3c653894fb7ab4c7780ec2527f4036f3f8781860194bd4fd003",
    "cross_cats_sorted": [
      "math.DS",
      "physics.chem-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T10:18:18Z",
    "title_canon_sha256": "b67181056bcb35241848d0ec40ec73b7b30a928644c0cc79e36e7fa2e32df786"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13305",
    "kind": "arxiv",
    "version": 1
  }
}