Reconstruction of stochastic dynamics from large streamed datasets.

Area of Science:

• Physics
• Applied Mathematics
• Data Science

Background:

• Complex physical systems are often modeled using stochastic differential equations (SDEs).
• Analyzing large time-series datasets from these systems is computationally challenging.
• Existing methods struggle with the scale of modern scientific data.

Purpose of the Study:

• To develop a computationally efficient method for estimating drift and diffusion functions from large time-series datasets.
• To overcome the limitations of traditional analysis techniques for complex systems.
• To enable the analysis of "big data" in scientific research.

Main Methods:

• Utilized incremental, online updating statistics for parameter estimation.
• Developed a novel algorithm for processing large datasets in a streaming fashion.
• Applied the method to synthetic and empirical datasets.

Main Results:

• Successfully estimated drift and diffusion functions from large synthetic datasets.
• Validated the method's utility on an empirical turbulence dataset.
• Demonstrated computational efficiency and accuracy compared to traditional methods.

Conclusions:

• The proposed online method effectively handles large-scale time-series data for SDE analysis.
• This approach facilitates the study of complex systems with "big data" and real-time streams.
• The method offers a scalable solution for dynamic system modeling.