Learning Stochastic Dynamics from Sparse Data with Geometric Constraints
Analysis
This paper addresses the challenge of learning the dynamics of stochastic systems from sparse, undersampled data. It introduces a novel framework that combines stochastic control and geometric arguments to overcome limitations of existing methods. The approach is particularly effective for overdamped Langevin systems, demonstrating improved performance compared to existing techniques. The incorporation of geometric inductive biases is a key contribution, offering a promising direction for stochastic system identification.
Key Takeaways
- •Proposes a new framework for learning stochastic dynamics from sparse data.
- •Combines stochastic control and geometric arguments.
- •Effective for overdamped Langevin systems.
- •Outperforms existing methods in benchmarks.
- •Highlights the importance of geometric inductive biases.
“Our method uses geometry-driven path augmentation, guided by the geometry in the system's invariant density to reconstruct likely trajectories and infer the underlying dynamics without assuming specific parametric models.”