2023/04/02 by Dimitra Maoutsa, Maoutsa, Dimitra
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #35B42 #37H05 #37M21 #82C99 #93E10 #93E12 #93E20 #Cell Image Analysis Techniques #Data Analysis #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #G.3 #Gaussian Processes and Bayesian Inference #I.6 #Machine Learning (cs.LG) #Methodology (stat.ME) #Model Reduction and Neural Networks #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2304.00423
openalex publication_date 2023/04/02 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28
The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the system's dynamics are observations at discrete points in time. Despite their widespread use, accurately inferring these systems from sparse-in-time observations remains challenging. Conventional inference methods either focus on the temporal structure of observations, neglecting the geometry of the system's invariant density, or use geometric approximations of the invariant density, which are limited to conservative driving forces. To address these limitations, here, we introduce a novel approach that reconciles these two perspectives. We propose a path augmentation scheme that employs data-driven control to account for the geometry of the invariant system's density. Non-parametric inference on the augmented paths, enables efficient identification of the underlying deterministic forces of systems observed at low sampling rates.