Advances in Stochastic Dynamics and Data Imputation

The field of stochastic dynamics and data imputation is rapidly advancing, with a focus on developing innovative methods for modeling and analyzing complex systems. Recent research has emphasized the importance of learning stochastic dynamics from data, particularly in cases where the system model is unknown or incomplete. Normalizing flows and diffusion models have emerged as powerful tools for density estimation and data imputation, enabling the development of more accurate and robust models. Notably, the use of adaptive dependency modeling and tensorial imputation has shown significant promise in improving the performance of spatio-temporal imputation methods. Furthermore, the application of diffusion models to data assimilation and physical dynamics has demonstrated the potential for more accurate and efficient state estimation and forecasting. Overall, the field is moving towards the development of more flexible and generalizable models that can handle complex, high-dimensional data and uncertain systems. Noteworthy papers include: Universal Learning of Stochastic Dynamics for Exact Belief Propagation using Bernstein Normalizing Flows, which establishes the theoretical foundations for a class of models that universally approximate general nonlinear stochastic dynamics and support analytical belief propagation. AdaSTI: Conditional Diffusion Models with Adaptive Dependency Modeling for Spatio-Temporal Imputation, which proposes a novel spatio-temporal imputation approach based on conditional diffusion models and achieves state-of-the-art performance on several real-world datasets.

Sources

Universal Learning of Stochastic Dynamics for Exact Belief Propagation using Bernstein Normalizing Flows

Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation

AdaSTI: Conditional Diffusion Models with Adaptive Dependency Modeling for Spatio-Temporal Imputation

Training-Free Data Assimilation with GenCast

Linear Regression under Missing or Corrupted Coordinates

Incomplete Data, Complete Dynamics: A Diffusion Approach

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