Pith Number

pith:B5UPK2T2

pith:2026:B5UPK2T2ENRWGBTDTFHLNZ6CUP

not attested not anchored not stored refs resolved

Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes

Harri L\"ahdesm\"aki, Julien Martinelli, Maksim Sinelnikov, M\'elanie Prague, Quentin Clairon

A Bayesian nonparametric model decomposes each subject's ODE vector field into a shared population Gaussian process and subject-specific deviations.

arxiv:2605.13088 v1 · 2026-05-13 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B5UPK2T2ENRWGBTDTFHLNZ6CUP}

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 controlled heterogeneous ODE benchmarks spanning oscillatory, biomedical systems, MEGPODE improves population-field recovery and subject-level trajectory prediction relative to strong baselines.

C2weakest assumption

The vector field of each subject can be usefully decomposed into a shared population component and a subject-specific deviation, both endowed with Gaussian process priors, and that virtual collocation observations suffice to avoid repeated ODE solves while preserving accurate posterior inference.

C3one line summary

MEGPODE decomposes subject-specific ODE vector fields into population and individual Gaussian process priors and uses Kalman smoothing with virtual collocation to enable efficient Bayesian mixed-effects inference for heterogeneous dynamical systems.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] Prediction of long- term humoral response induced by the two-dose heterologous ad26.zebov, mva-bn-filo vaccine against ebola.npj Vaccines, 2023 2023

[2] An amortized approach to non-linear mixed-effects modeling based on neural posterior estimation 2024

[3] Christopher M Bishop and Nasser M Nasrabadi.Pattern recognition and machine learning. Springer, 2006 2006

[4] Cambridge University Press 2004

[5] Dominic Stefan Bräm, Bernhard Steiert, Marc Pfister, Britta Steffens, and Gilbert Koch. Low- dimensional neural ordinary differential equations accounting for inter-individual variability implemented 2025

Receipt and verification

First computed	2026-05-18T03:08:58.494350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f68f56a7a2363630663994eb6e7c2a3de1cd84d9e63768e589bf0e4a8358684

Aliases

arxiv: 2605.13088 · arxiv_version: 2605.13088v1 · doi: 10.48550/arxiv.2605.13088 · pith_short_12: B5UPK2T2ENRW · pith_short_16: B5UPK2T2ENRWGBTD · pith_short_8: B5UPK2T2

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/B5UPK2T2ENRWGBTDTFHLNZ6CUP \
  | 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: 0f68f56a7a2363630663994eb6e7c2a3de1cd84d9e63768e589bf0e4a8358684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff2c44a4a7e7f8e5c7604b8545bd8350582873b5c20754ac33c1abc46528d368",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T06:57:01Z",
    "title_canon_sha256": "25ce04d30091fb7ebcdaedcab6e6a0aa9ee38e5b48a492b5e3a4005d5679c73e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13088",
    "kind": "arxiv",
    "version": 1
  }
}