Periodic Reporting for period 3 - NoMaMemo (Non-Markovian Memory-Based Modelling of Near- and Far-From-Equilibrium Dynamical Systems)
Reporting period: 2022-12-01 to 2024-05-31
We have also clarified how to derive the GLE from the underlying equations of motion, which is achieved by so-called projection techniques. Whereas the classical projection methods by Mori and Zwanzig led to rather unhandy expressions, we have by a novel hybrid projection technique derived an exact GLE whose parameters can all be extracted from time-series data in a unique manner. Our hybrid GLE contains a non-linear friction term, which has been neglected in previous works. With our exact formulation of the GLE, we can quantify the importance of the non-linear term and can therefore quantitatively assess whether its neglect is justified.
We have so far applied our GLE techniques to a variety of different systems: For the ultrafast vibrations of molecules, we have extracted the time-dependent friction acting on vibrating chemical bonds and can therefore predict infrared spectra in very good agreement with experiments. For the folding of proteins, we could show that non-Markovian friction effects not only determine the diffusional kinetics along the protein folding reaction coordinate but also show that friction memory modifies the folding times. Finally, for a stochastic searcher that tries to find randomly distributed targets, we show that memory of the search random walk improves the search efficiency in case the targets are distributed in a correlated fashion.
The expected results of the project are as follows. We plan to develop general techniques for extracting memory functions from time series data, including non-linear friction effects that could not be treated with previous methods. We will classify models as equilibrium or non-equilibrium. We will develop clustering techniques that will allow us to analyse single cells and organisms based on their movement patterns. Based on this we will be able to cluster and sort single cells and also make simple models for their internal network interactions and driving forces, based on the time dependence of the extracted memory function. We will develop techniques for memory-based time series prediction, we are currently testing these techniques on meteorological data and have achieved accuracies in predicting the weather that can compete with professional weather prediction tools. We will develop simulation methods to generate time series data based on memory models. These methods are essential to test our memory extraction tools. We will further develop our memory-based optimisation techniques for random walks. We will advance the memory-based modelling of reaction kinetics and protein folding dynamics. And finally, we will further develop memory-based techniques to predict infrared absorption spectra of complex solutions and molecules. We have already made significant advancements in all of these objectives.