Document detail
ID
oai:arXiv.org:2410.03108
Topic
Computer Science - Machine Learnin... Mathematics - Dynamical SystemsAuthor
Liu, Yanfang Chen, Yuan Xiu, Dongbin Zhang, GuannanCategory
Computer Science
Year
2024
listing date
10/9/2024
Keywords
model data stochastic systems diffusionAbstract
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data.
The proposed approach addresses key challenges in computational efficiency and accuracy for modeling SDEs by utilizing a score-based diffusion model to approximate their stochastic flow map.
Unlike the existing methods, this technique is based on an analytically derived closed-form exact score function, which can be efficiently estimated by Monte Carlo method using the trajectory data, and eliminates the need for neural network training to learn the score function.
By generating labeled data through solving the corresponding reverse ordinary differential equation, the approach enables supervised learning of the flow map.
Extensive numerical experiments across various SDE types, including linear, nonlinear, and multi-dimensional systems, demonstrate the versatility and effectiveness of the method.
The learned models exhibit significant improvements in predicting both short-term and long-term behaviors of unknown stochastic systems, often surpassing baseline methods like GANs in estimating drift and diffusion coefficients.
Liu, Yanfang,Chen, Yuan,Xiu, Dongbin,Zhang, Guannan, 2024, A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems
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