2023/01/19 by Dimitra Maoutsa, Maoutsa, Dimitra
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Data Analysis #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Methodology (stat.ME) #Protein Structure and Dynamics #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2301.08102
openalex publication_date 2023/01/19 · openalex created_date 2023/01/21 · openalex updated_date 2026/07/28
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations remains still a challenging endeavour. Existing approaches focus either on the temporal structure of the observations by relying on conditional expectations, discarding thereby information ingrained in the geometry of the system's invariant density; or employ geometric approximations of the invariant density, which are nevertheless restricted to systems with conservative forces. Here we propose a method that reconciles these two paradigms. We introduce a new data-driven path augmentation scheme that takes the local observation geometry into account. By employing non-parametric inference on the augmented paths, we can efficiently identify the deterministic driving forces of the underlying system for systems observed at low sampling rates.