Speaker
Description
Deviations from the standard laws of Brownian motion, the linear time dependence
of the mean squared displacement and the Gaussian probability density function,
are quite commonly observed in an adundance of systems. The physical mechanisms
for these anomalies are non-universal, prompting the need for different stochastic
models along with their identification from measured time series of dynamic
motion. The model classification and parameter regression of anomalous diffusion
can be successfully achieved by machine-learning tools such as Bayesian Deep
Learning [1], which will be introduced along with a brief summary of the two
recent AnDi (Anomalous Diffusion) Challenges [2].
The talk will mainly focus on long-range dependent stochastic motion, identified
in a large range of systems. In particular, it will be discussed how to generalise
such models to situations, in which the observed probability density function is
non-Gaussian and/or when the processes display scaling exponents varying in time
or space. Diffusion models with stochastically [3] and deterministically [4]
varying diffusion coefficients and scaling exponents will be introduced.
Applications to experimental data will be discussed.
References:
[1] H. Seckler and R. Metzler, Bayesian deep learning for error estimation
in the analysis of anomalous diffusion, Nature Commun. 13, 6717 (2022).
[2] G. Munoz-Gil et al, Objective comparison of methods to decode anomalous
diffusion, Nature Commun. 12, 6253 (2021); G. Munoz-Gil et al, Quantitative
evaluation of methods to analyze motion changes in single-particle experiments,
Nature Commun. 16, 6749 (2025).
[3] M. Balcerek, S. Thapa, K. Burnecki, H. Kantz, R. Metzler, A. Wylmanska,
and A. Chechkin, Multifractional Brownian motion with telegraphic,
stochastically varying exponent, Phys. Rev. Lett. 134, 197101 (2025).
[4] W. Wang, M. Balcerek, K. Burnecki, A. V. Chechkin, S. Janusonis, J
Slezak, T. Vojta, A. Wylmanska, and R. Metzler, Memory-multi-fractional
Brownian motion with continuous correlations, Phys. Rev. Res. 5, L032025
(2023).
