Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

Area of Science:

• Dynamical systems theory
• Nonlinear dynamics
• Stochastic processes

Background:

• Reconstructing dynamical models from time-series data is crucial for understanding complex systems.
• Existing methods often struggle with noise and require extensive parameter searches.
• Stochastic nonlinear dynamical systems present unique challenges due to inherent randomness and nonlinear interactions.

Purpose of the Study:

• To develop an analytical algorithm for reconstructing stochastic nonlinear dynamical models from noisy time-series data.
• To provide a method that avoids extensive global search for model parameters.
• To ensure optimal compensation for dynamical noise and robustness across various models.

Main Methods:

• An analytical approach is employed for model reconstruction.
• The algorithm directly infers model parameters without iterative global optimization.
• Dynamical noise effects are optimally compensated within the reconstruction process.

Main Results:

• The algorithm successfully inferred parameters for the stochastic Lorenz system, showing improved accuracy compared to previous research.
• Model reconstruction was demonstrated for a complex system of five globally and locally coupled noisy oscillators.
• The method proved efficient and accurate across different dynamical models.

Conclusions:

• The presented analytical algorithm offers a robust and efficient solution for reconstructing stochastic nonlinear dynamical models.
• This approach minimizes the need for computational செலவு (cost) associated with global parameter searches.
• The algorithm's effectiveness is validated on benchmark and complex systems, highlighting its practical applicability.