Non-Markovian Memory-Based Modelling of Near- and Far-From-Equilibrium Dynamical Systems

Descripción del proyecto

Comprender y predecir datos de series temporales

Las series temporales permiten caracterizar muchos sistemas, desde el movimiento de protones hasta el tipo de cambio dólar/yen. A fin de entender, comparar, clasificar y predecir datos de series temporales, las personas emplean, por lo general, ecuaciones diferenciales estocásticas, diversos modelos de caminos aleatorios y algoritmos de aprendizaje automático. Sin embargo, todos estos métodos dejan sin responder preguntas fundamentales. Para superar este problema, el objetivo del proyecto NoMaMemo, financiado con fondos europeos, es crear una plataforma genérica para analizar, comprender, comparar, clasificar y predecir datos de series temporales y optimizar sistemas estocásticos. Proporcionará una descripción unificada de datos genéricos de series temporales en términos de ecuaciones estocásticas integro-diferenciales no lineales basadas en funciones de memoria extraídas de datos. El proyecto, gracias su enfoque, mejorará sobremanera la comprensión de múltiples sistemas y procesos científicos.

Objetivo

Time series characterize diverse systems, examples in this proposal are: i) Proton motion in an inhomogeneous aqueous environment, ii) folding and unfolding of a peptide described by a suitably chosen reaction coordinate, iii) migration of a living cell on a substrate, iv) US Dollar / Yen exchange rate. Examples i) and ii) are close-to-equilibrium, iii) is a far from equilibrium since energy is constantly dissipated, while example iv) at first sight defies the classification into equilibrium or non-equilibrium.
For the understanding, comparison, classification and forecasting of time series data, stochastic differential equations, diverse random walk models, and more recently, machine-learning algorithms are commonly used. But fundamental questions remain unanswered: Is a unified description of such diverse systems possible? What is the relation between different proposed models? Can the non-equilibrium degree of a time series be estimated?
NoMaMemo provides a unified description of generic time series data in terms of non-linear integro-differential stochastic equations based on memory functions that are extracted from data. NoMaMemo accounts for non-linear and non-equilibrium effects as well as for non-Gaussian noise and connects with fundamental concepts such as equilibrium statistical mechanics, response theory and entropy production. The general formulation contains previously proposed models and thus allows their comparison, forecasting quality will be compared with modern machine-learning algorithms. NoMaMemo creates a generic platform to analyse, understand, compare, classify and predict time series data and to optimize stochastic systems with respect to search efficiency, barrier-crossing speed or other figures of merit. NoMaMemo will significantly advance the understanding of chemical reaction and protein folding kinetics, the interpretation of THz and IR spectroscopy of liquids and the analysis of living matter and socio-economic data.