Pith. sign in

REVIEW 1 cited by

A data-driven method for the steady state of randomly perturbed dynamics

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1805.04099 v2 pith:X4GUQDUJ submitted 2018-05-10 math.NA cs.NA

Yao Li This is my paper · ORCID
classification math.NAcs.NA
keywords methoddata-drivendensityfunctioninvariantnumericalperturbedprobability
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem corresponding to a reference solution, which is generated by Monte Carlo simulation. With this method we can solve for the invariant probability density function in any local area with high accuracy, regardless of whether the attractor is covered by the numerical domain.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions

    math.NA 2025-08 conditional novelty 6.0 of 10

    A data-driven ANN method estimates low-lying Fokker-Planck and Koopman eigenfunctions from Monte Carlo density relaxations, and is used to define a stochastic asymptotic phase for the noisy Lorenz system.

Pith tools