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arxiv_ml 95% Match Research Paper Researchers in stochastic processes,Machine learning practitioners,Quantitative analysts,Robotics engineers 1 week ago

Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

generative-ai › flow-models
📄 Abstract

Abstract: Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.
Authors (3)
Naoki Kiyohara
Edward Johns
Yingzhen Li
Submitted
October 29, 2025
arXiv Category
cs.LG
arXiv PDF

Key Contributions

This paper introduces Neural Stochastic Flows (NSFs), a solver-free approach to modeling and inference for Stochastic Differential Equations (SDEs). NSFs learn SDE transition laws directly using conditional normalizing flows, enabling efficient one-shot sampling between arbitrary states and achieving significant speed-ups while maintaining distributional accuracy.

Business Value

Enables faster and more efficient modeling of dynamic, noisy systems in fields like finance (e.g., risk modeling), robotics (e.g., trajectory prediction), and scientific simulation, leading to quicker insights and more responsive systems.

Paper Metadata

Innovation Type

Algorithmic Innovation

Deployment Feasibility

The solver-free nature and speed-ups make NSFs highly suitable for real-time applications and large-scale simulations, improving deployment feasibility in computationally demanding scenarios.

Limitations Addressed

The computational cost and complexity of traditional numerical solvers for sampling from SDEs, especially for irregularly sampled or noisy time series.

Performance Gains

Up to two orders of magnitude speed-up at large time gaps compared to numerical approaches.

Technical Tags

Stochastic Differential Equations (SDEs)Neural Stochastic Flows (NSFs)Normalizing FlowsSolver-Free InferenceTime Series ModelingLatent Variable ModelsOne-shot SamplingDistributional Accuracy

Research Topics

Stochastic ProcessesGenerative ModelingTime Series AnalysisDeep LearningProbabilistic Modeling

Methods & Architectures

Neural Stochastic Flows (NSFs)Conditional Normalizing FlowsSolver-free sampling Normalizing FlowsLatent Variable Models

Applications & Tasks

Finance Physics Machine Learning Robotics Computer Vision Modeling noisy/irregular time seriesEfficient sampling from SDEsReducing computational cost of SDE solvers Time series forecastingState estimationGenerative modeling of dynamic systems

Related Fields

Stochastic ProcessesDeep LearningTime Series AnalysisGenerative ModelsNumerical Analysis

Keywords

SDENeural Stochastic FlowsNormalizing flowsSolver-freeTime seriesGenerative modelsStochastic processesInferenceSamplingDynamic systemsFinanceRobotics

Academic Context

#Stochastic Processes#Generative Modeling#Time Series Analysis#Deep Learning#Probabilistic Modeling

Commercial Potential

Potential Products
Efficient simulation tools for financial marketsReal-time trajectory prediction systemsGenerative models for complex physical phenomena
Target Industries
FinanceRoboticsPhysicsAutomotiveAerospace
Use Case Examples
Modeling stock price movements with noisePredicting robot arm trajectoriesSimulating particle physics experiments
Competitive Edge
Offers a significant computational advantage over traditional SDE solvers by providing a solver-free, direct learning approach using normalizing flows.

Resource Requirements

Deployment Constraints
Requires careful tuning of normalizing flow architectures and training data representative of the SDE dynamics.
Scalability
The solver-free nature and speed-ups suggest good scalability for large time gaps and complex simulations.

Production Readiness

Maturity Level

Research

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