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Deep operator learning for efficient sampling from invariant measures of stochastic differential equations

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Updated 4 h ago · first seen 11 Sept 2026

paper_01M294FQX2NGSR66RC46MVMCYX

Published: 11 Sept 2026; T1 · 4 h ago
arXiv: 2609.11376; T1 · 4 h ago
Category: math.NA; T1 · 4 h ago

Abstract

We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.

Authors 3

Lin Guo, Li Lei, Jingtong Zhang

Specification

Official page: arxiv.org/abs/2609.11376
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
arXiv id: 2609.11376
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Categories: math.NA, cs.LG, cs.NA
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
PDF: arxiv.org/pdf/2609.11376
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Primary category: math.NA
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh

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T19

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4 h ago

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Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
We introduce an amortized neural sampler that combines operator learning with flow methods for sampling. It maps SDE coefficient functions to pushforwards from a reference measure to the invariant measures, enabling efficient sampling across families of stochastic differential equations. Our framework shifts traditional sampling cost to an initial training phase, after which new SDE instances require only one encoder pass and a few ODE solver steps, independent of mixing time. To handle problems in high dimensions, we use Lagrangian trajectory sensors for the coefficient functions and cross attention in the architecture. We also theoretically establish the expressivity and resolution invariance of our framework. Experiments on 1D and 2D SDE families show competitive accuracy with substantial speedups over MCMC in regimes with slow mixing, transfer across sensor counts, and demonstration results on a 64D interacting particle SDE where traditional grid approaches are infeasible.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	2 h ago	1

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