Project description
Understanding and predicting time series data
Time series characterise diverse systems that can range from proton motion to the Dollar/Yen exchange rate. To understand, compare, classify and forecast time series data, people commonly use stochastic differential equations, diverse random walk models and machine-learning algorithms but these leave fundamental questions unanswered. To overcome this problem, the EU-funded NoMaMemo project aims to create a generic platform to analyse, understand, compare, classify and predict time series data and to optimise stochastic systems. It will provide a unified description of generic time series data in terms of non-linear integro-differential stochastic equations based on memory functions extracted from data. Through its approach, the project will significantly advance the understanding of multiple scientific systems and processes.
Objective
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.
Fields of science
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations
- natural sciencesmathematicsapplied mathematicsdynamical systems
- natural sciencesbiological sciencesbiochemistrybiomoleculesproteinsprotein folding
- natural sciencesphysical sciencesclassical mechanicsstatistical mechanics
- natural sciencescomputer and information sciencesartificial intelligencemachine learning
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Funding Scheme
ERC-ADG - Advanced GrantHost institution
14195 Berlin
Germany