2018/10/17 by Michał Branicki, Michal Branicki, Branicki, Michal +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Information Theory (cs.IT) #Model Reduction and Neural Networks #Probability (math.PR) #Topological and Geometric Data Analysis #cs.IT #math.DS #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.1810.07567
openalex publication_date 2018/10/17 · arxiv created 2021/12/23 · arxiv updated 2021/12/24 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian (trajectory-based) predictions. These expansion rates are quantified via certain divergences (pre-metrics) between probability measures induced by the laws of the stochastic flow associated with the underlying dynamics. We construct scalar fields of finite-time divergence/expansion rates, show their existence and space-time continuity for general stochastic flows. Combining these divergence rate fields with our 'information inequalities' derived in allows for quantification and mitigation of the uncertainty in path-based observables estimated from simplified models in a way that is amenable to algorithmic implementations, and it can be utilised in information-geometric analysis of statistical estimation and inference, as well as in a data-driven machine/deep learning of coarse-grained models. We also derive a link between the divergence rates and finite-time Lyapunov exponents for probability measures and for path-based observables.