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DY: Fachverband Dynamik und Statistische Physik

DY 4: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications I

DY 4.3: Vortrag

Montag, 17. März 2025, 10:15–10:30, H43

Towards a model-free inference of hidden states and transition pathways — •Xizhu Zhao¹, Dmitrii E. Makarov², and Aljaž Godec¹ — ¹Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany — ²University of Texas at Austin, Austin, Texas, USA

Experiments on biophysical systems typically probe lower-dimensional observables, which are projections of high-dimensional dynamics. In order to infer a consistent model capturing the relevant dynamics of the system, it is important to detect and account for the memory in the dynamics. We develop a method to infer the presence of hidden states and transition pathways based on transition probabilities between observable states conditioned on history sequences for projected (i.e. observed) dynamics of Markov chains. The histograms conditioned on histories reveal information on the transition probabilities of hidden paths locally between any specific pair of states, including the duration of memory. The method can be used to test the local Markov property of observables. The information extracted is also helpful in inferring relevant hidden transitions which are not captured by a Markov-state model.

Keywords: projected dynamics; memory; hidden states; hidden transition paths