Bayesian inference for geophysical fluid dynamics using generative models.

Area of Science:

• Computational Mathematics
• Scientific Computing
• Data Assimilation

Background:

• Data assimilation is vital for enhancing numerical model accuracy by integrating real-world observations.
• Calibrating high-dimensional, nonlinear systems presents significant computational challenges.

Purpose of the Study:

• To present a novel calibration approach for complex systems using diffusion generative models.
• To demonstrate efficient model reduction and data assimilation in high-dimensional systems.

Main Methods:

• Utilized diffusion generative models to produce synthetic data aligned with numerical solutions.
• Applied these synthetic samples for model reduction of a high-resolution rotating shallow water equation.
• Integrated samples into an enhanced particle filtering method with tempering and jittering.

Main Results:

• Generative models effectively produced synthetic data for calibrating complex systems.
• Achieved efficient data assimilation from a high-dimensional system (10^4 degrees of freedom) to a reduced stochastic system.
• Demonstrated improved particle filter accuracy and computational efficiency.

Conclusions:

• Diffusion generative models offer a computationally efficient solution for data assimilation and model calibration.
• The proposed method enhances the accuracy and predictive capabilities of numerical simulations.
• This approach represents a significant advancement for inverse problems in generative modeling and Bayesian inference.